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Core Shells and Double Bubbles in a Weighted Nonlocal Isoperimetric Problem SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-15 Stanley Alama, Lia Bronsard, Xinyang Lu, Chong Wang
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 2357-2394, April 2024. Abstract. We consider a sharp-interface model of [math] triblock copolymers, for which the surface tension [math] across the interface separating phase [math] from phase [math] may depend on the components. We study global minimizers of the associated ternary local isoperimetric problem in [math], and show how the
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Weak and Renormalized Solutions to a Hypoelliptic Mean Field Games System SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-15 Nikiforos Mimikos-Stamatopoulos
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 2312-2356, April 2024. Abstract. We study the well-posedness of a degenerate, hypoelliptic Mean Field Games system with local coupling and Hamiltonians which either are Lipschitz or grow quadratically in the gradient. In the former case, we prove the existence and uniqueness of weak solutions, while in the latter we study the same question
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Contour Dynamics and Global Regularity for Periodic Vortex Patches and Layers SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-14 David M. Ambrose, Fazel Hadadifard, James P. Kelliher
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 2286-2311, April 2024. Abstract. We study vortex patches for the two-dimensional incompressible Euler equations. Prior works on this problem take the support of the vorticity (i.e., the vortex patch) to be a bounded region. We instead consider the horizontally periodic setting. This includes both the case of a periodic array of bounded
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Sharp Nonuniqueness of Solutions to Stochastic Navier–Stokes Equations SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-14 Weiquan Chen, Zhao Dong, Xiangchan Zhu
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 2248-2285, April 2024. Abstract. In this paper we establish a sharp nonuniqueness result for stochastic [math]-dimensional ([math]) incompressible Navier–Stokes equations. First, for every divergence-free initial condition in [math] we show existence of infinitly many global-in-time probabilistically strong and analytically weak solutions
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Existence and Stability of Dissipative Measure-Valued Solutions to the Full Compressible Magnetohydrodynamic Flows SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-13 Bingkang Huang
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 2213-2247, April 2024. Abstract.In this paper, we are concerned with dissipative measure-valued (DMV) solutions to the full compressible magnetohydrodynamics. The existence of the DMV solutions is established. Moreover, we prove that the strong solutions are stable in this class of generalized solution. Specifically, we demonstrate that
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Blow-Up vs. Global Existence for a Fujita-Type Heat Exchanger System SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-13 Samuel Tréton
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 2191-2212, April 2024. Abstract. We analyze a reaction-diffusion system on [math] which models the dispersal of individuals between two exchanging environments for its diffusive component and incorporates a Fujita-type growth for its reactive component. The originality of this model lies in the coupling of the equations through diffusion
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Square Root Normal Fields for Lipschitz Surfaces and the Wasserstein Fisher Rao Metric SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-08 Emmanuel Hartman, Martin Bauer, Eric Klassen
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 2171-2190, April 2024. Abstract. The square root normal field (SRNF) framework is a method in the area of shape analysis that defines a (pseudo)distance between unparametrized surfaces. For piecewise linear surfaces it was recently proved that the SRNF distance between unparametrized surfaces is equivalent to the Wasserstein Fisher Rao
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The Scattering Resonances for Schrödinger-Type Operators with Unbounded Potentials SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-07 Peijun Li, Xiaohua Yao, Yue Zhao
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 2149-2170, April 2024. Abstract. This paper addresses the meromorphic continuation of the outgoing resolvent associated with Schrödinger-type operators in three dimensions. The first part focuses on the classical Schrödinger-type operator involving unbounded potentials. The absence of nonzero real poles for the outgoing resolvent is investigated
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Inverse Resonance Problems for Energy-Dependent Potentials on the Half-Line SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-05 Evgeny Korotyaev, Andrea Mantile, Dmitrii Mokeev
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 2115-2148, April 2024. Abstract. We consider Schrödinger equations with energy-dependent potentials that are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under suitable regularity assumptions. Then, we consider a specific class of energy-dependent
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A Degenerate Cross-Diffusion System as the Inviscid Limit of a Nonlocal Tissue Growth Model SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-05 Noemi David, Tomasz Dębiec, Mainak Mandal, Markus Schmidtchen
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 2090-2114, April 2024. Abstract. In recent years, there has been a spike in interest in multiphase tissue growth models. Depending on the type of tissue, the velocity is linked to the pressure through Stoke’s law, Brinkman’s law, or Darcy’s law. While each of these velocity-pressure relations has been studied in the literature, little
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Analysis of a Dilute Polymer Model with a Time-Fractional Derivative SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-04 Marvin Fritz, Endre Süli, Barbara Wohlmuth
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 2063-2089, April 2024. Abstract. We investigate the well-posedness of a coupled Navier–Stokes–Fokker–Planck system with a time-fractional derivative. Such systems arise in the kinetic theory of dilute solutions of polymeric liquids, where the motion of noninteracting polymer chains in a Newtonian solvent is modeled by a stochastic process
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Monotonicity Properties of Limits of Solutions to the Semidiscrete Scheme for a Class of Perona–Malik Type Equations SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-04 Massimo Gobbino, Nicola Picenni
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 2034-2062, April 2024. Abstract. We consider generalized solutions of the Perona–Malik equation in dimension one, defined as all possible limits of solutions to the semidiscrete approximation in which derivatives with respect to the space variable are replaced by difference quotients. Our first result is a pathological example in which
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Steady States with Jump Discontinuity in a Receptor-Based Model with Hysteresis in Higher-Dimensional Domains SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-04 Goro Akagi, Izumi Takagi, Conghui Zhang
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1996-2033, April 2024. Abstract. This paper deals with a receptor-based model which arises from the modeling of interactions between intracellular processes and diffusible signaling factors. We prove the existence of stationary solutions with jump discontinuity by a variational method. Then a singular perturbation problem with discontinuous
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Inverse Scattering for the Biharmonic Wave Equation with a Random Potential SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-04 Peijun Li, Xu Wang
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1959-1995, April 2024. Abstract. We consider the inverse random potential scattering problem for the two- and three-dimensional biharmonic wave equation in lossy media. The potential is assumed to be a microlocally isotropic Gaussian rough field. The main contributions of the work are twofold. First, the unique continuation principle is
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Almost Global Existence for Kirchhoff Equations Around Global Solutions SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-04 Marina Ghisi, Massimo Gobbino
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1936-1958, April 2024. Abstract. It is well-known that the life span of solutions to Kirchhoff equations tends to infinity when initial data tend to zero. These results are usually referred to as almost global existence, at least in a neighborhood of the null solution. Here we extend this result by showing that the life span of solutions
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Nonlocal Bounded Variations with Applications SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-04 Harbir Antil, Hugo Díaz, Tian Jing, Armin Schikorra
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1903-1935, April 2024. Abstract. Motivated by problems where jumps across lower dimensional subsets and sharp transitions across interfaces are of interest, this paper studies the properties of fractional bounded variation ([math])-type spaces. Two different natural fractional analogs of classical [math] are considered: [math], a space
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On the Global Well-Posedness for the Periodic Quintic Nonlinear Schrödinger Equation SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-04 Xueying Yu, Haitian Yue
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1851-1902, April 2024. Abstract. In this paper, we consider the initial value problem for the quintic, defocusing nonlinear Schrödinger equation on [math] with general data in the critical Sobolev space [math]. We show that if a solution remains bounded in [math] in its maximal interval of existence, then the solution exists globally in
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Initial-Boundary Value Problems for Poiseuille Flow of Nematic Liquid Crystal via Full Ericksen–Leslie Model SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-01 Geng Chen, Yanbo Hu, Qingtian Zhang
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1809-1850, April 2024. Abstract. In this paper, we study the initial-boundary value problem for the Poiseuille flow of a hyperbolic-parabolic Ericksen–Leslie model of nematic liquid crystals in one space dimension. We consider a simplified system by restricting the Leslie coefficients to special cases such that some quantities are constants
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Asymptotic Expansion of the Spectrum for Periodic Schrödinger Operators SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-01 Scott Armstrong, Raghavendra Venkatraman
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1770-1808, April 2024. Abstract. We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schrödinger-type operator with a confining potential and with the principle part of a periodic elliptic operator in divergence form. We compare the spectrum to the homogenized operator and characterize the corrections up to arbitrarily
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Minimal Mass Blow-Up Solutions for the [math]-Critical NLS with the Delta Potential for Even Data in One Dimension SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-01 Xingdong Tang, Guixiang Xu
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1727-1769, April 2024. Abstract. We consider the [math]-critical nonlinear Schrödinger equation (NLS) with the delta potential [math] where [math] and [math] is the Dirac delta distribution at [math]. Local well-posedness theory, together with the sharp Gagliardo–Nirenberg inequality and the conservation laws of mass and energy, implies
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Global Dynamics to the Periodic Ferromagnetic Spin Chain System SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-01 Li Ze, Changzheng Qu
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1672-1726, April 2024. Abstract. In this paper, we study the dynamical system driven by the ferromagnetic spin chain system defined in [math] with or without external fields. In the first part, we prove the convergence to equilibriums for arbitrary large initial data of finite energy and prove the existence of heteroclinic orbits emerging
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Evolution of Dispersal in Advective Homogeneous Environments: Inflow Versus Outflow SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-01 Yin Wang, Qingxiang Xu, Peng Zhou
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1643-1671, April 2024. Abstract. We consider a single species model and a two species competition model in one-dimensional open advective environments featured by an inflow (resp., outflow) of individuals at the upstream (resp., downstream) end as measured by a parameter [math] (resp., [math]). The two species are assumed to follow the
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Torsional Rigidity in Random Walk Spaces SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-01 José M. Mazón, Julián Toledo
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1604-1642, April 2024. Abstract. In this paper we study the (nonlocal) torsional rigidity in the ambient space of random walk spaces. We get the relation of the (nonlocal) torsional rigidity of a set [math] with the spectral [math]-heat content of [math], which gives rise to a complete description of the nonlocal torsional rigidity of
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Fuglede-Type Arguments for Isoperimetric Problems and Applications to Stability Among Convex Shapes SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-01 Raphaël Prunier
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1560-1603, April 2024. Abstract.This paper is concerned with the stability of the ball for a class of isoperimetric problems under a convexity constraint. Considering the problem of minimizing [math] among convex subsets of [math] of fixed volume, where [math] is the perimeter functional, [math] is a perturbative term, and [math] is a
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Modulated Energy Estimates for Singular Kernels and their Applications to Asymptotic Analyses for Kinetic Equations SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-01 Young-Pil Choi, Jinwook Jung
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1525-1559, April 2024. Abstract. In this paper, we provide modulated interaction energy estimates for the kernel [math] with [math] and its applications to quantified asymptotic analyses for kinetic equations. The proof relies on a dimension extension argument for an elliptic operator and its commutator estimates. For the applications
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Poisson Equation on Wasserstein Space and Diffusion Approximations for Multiscale McKean–Vlasov Equation SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-03-01 Yun Li, Fuke Wu, Longjie Xie
SIAM Journal on Mathematical Analysis, Volume 56, Issue 2, Page 1495-1524, April 2024. Abstract. We consider the fully-coupled McKean–Vlasov equation with multi-time-scale potentials, and all the coefficients depend on the distributions of both the slow component and the fast motion. By studying the smoothness of the solution of the Poisson equation on Wasserstein space, we derive the asymptotic limit
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Integrability Propagation for a Boltzmann System Describing Polyatomic Gas Mixtures SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-02-15 Ricardo Alonso, Milana Čolić
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 1459-1494, February 2024. Abstract. This paper explores the [math] Lebesgue’s integrability propagation, [math], of a system of space homogeneous Boltzmann equations modelling a multicomponent mixture of polyatomic gases based on the continuous internal energy. For typical collision kernels proposed in the literature, [math] moment-entropy-based
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Global Well-Posedness and Scattering for Fourth-Order Schrödinger Equations on Waveguide Manifolds SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-02-12 Xueying Yu, Haitian Yue, Zehua Zhao
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 1427-1458, February 2024. Abstract. In this paper, we study the well-posedness theory and the scattering asymptotics for fourth-order Schrödinger equations (4NLS) on waveguide manifolds (semiperiodic spaces) [math], [math], [math]. The torus component [math] can be generalized to [math]-dimensional compact manifolds [math]. First, we modify
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Propagation of Moments and Sharp Convergence Rate for Inhomogeneous Noncutoff Boltzmann Equation with Soft Potentials SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-02-09 Chuqi Cao, Ling-Bing He, Jie Ji
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 1321-1426, February 2024. Abstract. We prove the well-posedness for the noncutoff Boltzmann equation with soft potentials when the initial datum is close to the global Maxwellian and has only polynomial decay at the large velocities in [math] space. As a result, we get the propagation of the exponential moments and the sharp rates of the
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Isothermal Limit of Entropy Solutions of the Euler Equations for Isentropic Gas Dynamics SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-02-08 Gui-Qiang G. Chen, Fei-Min Huang, Tian-Yi Wang
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 1300-1320, February 2024. Abstract. We are concerned with the isothermal limit of entropy solutions in [math], containing the vacuum states, of the Euler equations for isentropic gas dynamics. We prove that the entropy solutions in [math] of the isentropic Euler equations converge strongly to the corresponding entropy solutions of the
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A Regularity Theory for Parabolic Equations with Anisotropic Nonlocal Operators in [math] Spaces SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-02-06 Jae-Hwan Choi, Jaehoon Kang, Daehan Park
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 1264-1299, February 2024. Abstract. In this paper, we present an [math]-regularity theory for parabolic equations of the form [math] Here, [math] represents anisotropic nonlocal operators encompassing the singular anisotropic fractional Laplacian with measurable coefficients: [math] To address the anisotropy of the operator, we employ
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Global [math] Estimates for Kinetic Kolmogorov–Fokker–Planck Equations in Divergence Form SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-31 Hongjie Dong, Timur Yastrzhembskiy
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 1223-1263, February 2024. Abstract. We present a priori estimates and unique solvability results in the mixed-norm Lebesgue spaces for the kinetic Kolmogorov–Fokker–Planck (KFP) equation in divergence form. The leading coefficients are bounded uniformly nondegenerate with respect to the velocity variable [math] and satisfy a vanishing
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Bistable Wavefronts in the Delayed Belousov–Zhabotinsky Reaction SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-31 Karel Hasík, Jana Kopfová, Petra Nábělková, Sergei Trofimchuk
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 1197-1222, February 2024. Abstract. We study the Murray adaptation of the Noyes–Field five-step model of the Belousov–Zhabotinsky (BZ) reaction in the case when a tuning parameter [math], which determines the level of the bromide ion far ahead of the propagating wave, is bigger than 1 and when the delay in generation of the bromous acid
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Two Slope Functions Minimizing Fractional Seminorms and Applications to Misfit Dislocations SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-31 Lucia De Luca, Marcello Ponsiglione, Emanuele Spadaro
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 1179-1196, February 2024. Abstract. We consider periodic piecewise affine functions, defined on the real line, with two given slopes, one positive and one negative, and prescribed length scale of the intervals where the slope is negative. We prove that, in such a class, the minimizers of [math]-fractional Gagliardo seminorm densities,
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Shearing Viscoelasticity in Partially Dissipative Timoshenko–Boltzmann Systems SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-31 Eduardo H. Gomes Tavares, Marcio A. Jorge Silva, To Fu Ma, Higidio P. Oquendo
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 1149-1178, February 2024. Abstract. We investigate both the mathematical modeling and stability methods for a new integro-differential system referred to as the viscoelastic Timoshenko–Boltzmann model. The modeling is developed for materials with hereditary memory under the creation time scenario whose foundation goes back to Boltzmann’s
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An Optimal Transport Analogue of the Rudin–Osher–Fatemi Model and Its Corresponding Multiscale Theory SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-31 Tristan Milne, Adrian Nachman
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 1114-1148, February 2024. Abstract. In the first part of this paper we develop a theory for image restoration with a learned regularizer that is analogous to that of Meyer’s geometric characterization of solutions of the classical variational method of Rudin–Osher–Fatemi (ROF). The learned regularizer we use is a Kantorovich potential
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Mean-Field Limit Derivation of a Monokinetic Spray Model with Gyroscopic Effects SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-31 Matthieu Ménard
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 1068-1113, February 2024. Abstract. In this paper we derive a two dimensional spray model with gyroscopic effects as the mean-field limit of a system modeling the interaction between an incompressible fluid and a finite number of solid particles. This spray model has been studied by Moussa and Sueur in [Asymptot. Anal., 81 (2013), pp.
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Dynamics and Large Deviations for Fractional Stochastic Partial Differential Equations with Lévy Noise SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-29 Jiaohui Xu, Tomás Caraballo, José Valero
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 1016-1067, February 2024. Abstract. This paper is mainly concerned with a kind of fractional stochastic evolution equations driven by Lévy noise in a bounded domain. We first state the well-posedness of the problem via iterative approximations and energy estimates. Then, the existence and uniqueness of weak pullback mean random attractors
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Asymptotic Behavior of Solutions to the Cauchy Problem for 1D [math]-System with Space-Dependent Damping SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-25 Akitaka Matsumura, Kenji Nishihara
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 993-1015, February 2024. Abstract. We consider the Cauchy problem for a one-dimensional [math]-system with damping of space-dependent coefficient. This system models the compressible flow through porous media in the Lagrangian coordinate. Our concern is an asymptotic behavior of solutions, which is expected to be the diffusion wave based
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The Magnetic Liouville Equation as a Semiclassical Limit SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-19 Immanuel Ben Porat
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 955-992, February 2024. Abstract. The Liouville equation with nonconstant magnetic field is obtained as a limit in the Planck constant [math] of the von Neumann equation with the same magnetic field. The convergence is with respect to an appropriate semiclassical pseudodistance, and consequently with respect to the Monge–Kantorovich distance
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Quantitative Coarse-Graining of Markov Chains SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-18 Bastian Hilder, Upanshu Sharma
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 913-954, February 2024. Abstract. Coarse-graining techniques play a central role in reducing the complexity of stochastic models and are typically characterized by a mapping which projects the full state of the system onto a smaller set of variables which captures the essential features of the system. Starting with a continuous-time Markov
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Nonlocal Double Phase Implicit Obstacle Problems with Multivalued Boundary Conditions SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-17 Shengda Zeng, Vicenţiu D. Rădulescu, Patrick Winkert
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 877-912, February 2024. Abstract. In this paper, we consider a mixed boundary value problem with a nonhomogeneous, nonlinear differential operator (called double phase operator), a nonlinear convection term (a reaction term depending on the gradient), three multivalued terms, and an implicit obstacle constraint. Under very general assumptions
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The Vlasov–Poisson–Boltzmann/Landau System with Polynomial Perturbation Near Maxwellian SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-16 Chuqi Cao, Dingqun Deng, Xingyu Li
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 820-876, February 2024. Abstract. In this work, we consider the Vlasov–Poisson–Boltzmann system without angular cutoff and the Vlasov–Poisson–Landau system with Coulomb potential near a global Maxwellian [math] in a torus or union of cubes. We establish the global existence, uniqueness, and large-time behavior for solutions in a polynomial-weighted
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Weakly Nonlinear Geometric Optics for the Westervelt Equation and Recovery of the Nonlinearity SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-16 Nikolas Eptaminitakis, Plamen Stefanov
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 801-819, February 2024. Abstract. We study the nondiffusive Westervelt equation in the weakly nonlinear regime and show that the leading profile equation is of Burgers’ type. We show that a compactly supported nonlinearity coefficient [math] can be reconstructed from the tilt of the transmitted high frequency wave packets sent from different
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An [math] Approach for the Non-Cutoff Boltzmann Equation in [math] SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-16 Renjun Duan, Shota Sakamoto, Yoshihiro Ueda
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 762-800, February 2024. Abstract. In the paper, we develop an [math] approach to construct global solutions to the Cauchy problem on the non-cutoff Boltzmann equation near equilibrium in [math]. In particular, only smallness of [math] with [math] is imposed on initial data [math], where [math] is the Fourier transform in space variable
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On a Model of an Elastic Body Fully Immersed in a Viscous Incompressible Fluid with Small Data SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-12 Igor Kukavica, Wojciech S. Ożański
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 746-761, February 2024. Abstract. We consider a model of an elastic body immersed between two layers of incompressible viscous fluid. The elastic displacement [math] is governed by the damped wave equation [math] without any stabilization terms, where [math], and the fluid is modeled by the Navier–Stokes equations. We assume continuity
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Reconstruction of Cracks in Calderón’s Inverse Conductivity Problem Using Energy Comparisons SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-12 Henrik Garde, Michael Vogelius
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 727-745, February 2024. Abstract. We derive exact reconstruction methods for cracks consisting of unions of Lipschitz hypersurfaces in the context of Calderón’s inverse conductivity problem. Our first method obtains upper bounds for the unknown cracks, bounds that can be shrunk to obtain the exact crack locations upon verifying certain
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A Simplified Voltage-Conductance Kinetic Model for Interacting Neurons and Its Asymptotic Limit SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-11 José A. Carrillo, Xu’an Dou, Zhennan Zhou
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 676-726, February 2024. Abstract. The voltage-conductance kinetic model for the collective behavior of neurons has been studied by scientists and mathematicians for two decades, but the rigorous analysis of its solution structure has been only partially obtained in spite of plenty of numerical evidence in various scenarios. In this work
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Entropy Solutions to the Dirichlet Problem for Nonlinear Diffusion Equations with Conservative Noise SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-11 Kai Du, Ruoyang Liu, Yuxing Wang
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 637-675, February 2024. Abstract. Motivated by porous medium equations with a randomly perturbed velocity field, this paper considers a class of nonlinear degenerate diffusion equations with nonlinear conservative noise in bounded domains. The existence, uniqueness, and [math]-stability of nonnegative entropy solutions under the homogeneous
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Lipschitz Stability Estimate and Uniqueness in the Retrospective Analysis for the Mean Field Games System via Two Carleman Estimates SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-11 Michael V. Klibanov, Yurii Averboukh
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 616-636, February 2024. Abstract. A retrospective analysis process for the mean field games system (MFGS) is considered. For the first time, Carleman estimates are applied to the analysis of the MFGS. Two new Carleman estimates are derived. They allow us to obtain the Lipschitz stability estimate with respect to a possible error in the
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Stability of the Ball for Attractive-Repulsive Energies SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-11 Marco Bonacini, Riccardo Cristoferi, Ihsan Topaloglu
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 588-615, February 2024. Abstract. We consider a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. It has recently been proved by Frank and Lieb that the ball is the unique (up to translation) global minimizer for sufficiently large mass. We
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Kinetic Chemotaxis Tumbling Kernel Determined from Macroscopic Quantities SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-10 Kathrin Hellmuth, Christian Klingenberg, Qin Li, Min Tang
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 568-587, February 2024. Abstract. Chemotaxis is the physical phenomenon that bacteria adjust their motions according to chemical stimulus. A classical model for this phenomenon is a kinetic equation that describes the velocity jump process whose tumbling/transition kernel uniquely determines the effect of a chemical stimulus on bacteria
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Improved Concentration of Laguerre and Jacobi Ensembles SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-09 Yichen Huang (黄溢辰), Aram W. Harrow
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 554-567, February 2024. Abstract. We consider the asymptotic limits where certain parameters in the definitions of the Laguerre and Jacobi ensembles diverge. In these limits, Dette, Imhof, and Nagel proved that, up to a linear transformation, the joint probability distributions of the ensembles become more and more concentrated around
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Mean Field Games Systems under Displacement Monotonicity SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-09 Alpár R. Mészáros, Chenchen Mou
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 529-553, February 2024. Abstract. In this note we prove the uniqueness of solutions to a class of mean field games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general nonseparable Hamiltonians that satisfy a so-called displacement monotonicity condition. This monotonicity
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Global Existence for the Stochastic Boussinesq Equations with Transport Noise and Small Rough Data SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-09 Quyuan Lin, Rongchang Liu, Weinan Wang
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 501-528, February 2024. Abstract. In this paper, we consider the stochastic Boussinesq equations on [math] with transport noise and rough initial data. We prove the existence and uniqueness of the local pathwise solution with initial data in [math] for [math]. By assuming additional smallness on the initial data and the noise, we establish
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Sharp Behavior of Dirichlet–Laplacian Eigenvalues for a Class of Singularly Perturbed Problems SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-09 Laura Abatangelo, Roberto Ognibene
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 474-500, February 2024. Abstract. We deepen the study of Dirichlet eigenvalues in bounded domains where a thin tube is attached to the boundary. As its section shrinks to a point, the problem is spectrally stable and we quantitatively investigate the rate of convergence of the perturbed eigenvalues. We detect the proper quantity which
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Polarized High-frequency Wave Propagation Beyond the Nonlinear Schrödinger Approximation SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-09 Julian Baumstark, Tobias Jahnke, Christian Lubich
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 454-473, February 2024. Abstract. This paper studies highly oscillatory solutions to a class of systems of semilinear hyperbolic equations with a small parameter, in a setting that includes Klein–Gordon equations and the Maxwell–Lorentz system. The interest here is in solutions that are polarized in the sense that up to a small error,
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Stability for Time-Domain Elastic Wave Equations SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-08 Bochao Chen, Yixian Gao, Shuguan Ji, Yang Liu
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 433-453, February 2024. Abstract. This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded [math]-dimensional domain. First, an explicit formula for the density reconstruction is established by means of the Dirichlet-to-Neumann operator. The reconstruction is mainly based
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Forced Rapidly Dissipative Navier–Stokes Flows SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-08 Lorenzo Brandolese, Takahiro Okabe
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 412-432, February 2024. Abstract. We show that, by acting on a finite number of parameters of a compactly supported control force, we can increase the energy dissipation rate of any small solution of the Navier–Stokes equations in [math]. The magnitude of the control force is bounded by a negative Sobolev norm of the initial velocity.
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A Generalized Beale–Kato–Majda Breakdown Criterion for the Free-Boundary Problem in Euler Equations with Surface Tension SIAM J. Math. Anal. (IF 2.0) Pub Date : 2024-01-08 Chenyun Luo, Kai Zhou
SIAM Journal on Mathematical Analysis, Volume 56, Issue 1, Page 374-411, February 2024. Abstract. It is shown in Ferrari [Comm. Math. Phys., 155 (1993), pp. 277–294] that if [math] is the maximal time interval of existence of a smooth solution of the incompressible Euler equations in a bounded, simply connected domain in [math], then [math], where [math] is the vorticity of the flow. Ferrari’s result