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On the high friction limit for the complete Euler system J. Evol. Equ. (IF 1.4) Pub Date : 2024-03-15 Eduard Feireisl, Piotr Gwiazda, Young-Sam Kwon, Agnieszka Świerczewska-Gwiazda
We show that solutions of the complete Euler system of gas dynamics perturbed by a friction term converge to a solution of the porous medium equation in the high friction/long time limit. The result holds in the largest possible class of generalized solutions–the measure–valued solutions of the Euler system.
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Existence of a unique global solution, and its decay at infinity, for the modified supercritical dissipative quasi-geostrophic equation J. Evol. Equ. (IF 1.4) Pub Date : 2024-03-15 Wilberclay G. Melo
Our interest in this research is to prove the decay, as time tends to infinity, of a unique global solution for the supercritical case of the modified quasi-gesotrophic equation (MQG) $$\begin{aligned} \theta _t \;\!+\, (-\Delta )^{\alpha }\,\theta \,+\, u_{\theta } \cdot \nabla \theta \;=\; 0, \quad \hbox {with } u_{\theta }\;=\;(\partial _2(-\Delta )^{\frac{\gamma -2}{2}}\theta , -\partial _1(-\Delta
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A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects J. Evol. Equ. (IF 1.4) Pub Date : 2024-03-15 Christian Stinner, Michael Winkler
The quasilinear Keller–Segel system $$\begin{aligned} \left\{ \begin{array}{l} u_t=\nabla \cdot (D(u)\nabla u) - \nabla \cdot (S(u)\nabla v), \\ v_t=\Delta v-v+u, \end{array}\right. \end{aligned}$$ endowed with homogeneous Neumann boundary conditions is considered in a bounded domain \(\Omega \subset {\mathbb {R}}^n\), \(n \ge 3\), with smooth boundary for sufficiently regular functions D and S satisfying
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The Stokes Dirichlet-to-Neumann operator J. Evol. Equ. (IF 1.4) Pub Date : 2024-03-15 C. Denis, A. F. M. ter Elst
Let \(\Omega \subset \mathbb {R}^d\) be a bounded open connected set with Lipschitz boundary. Let \(A^N\) and \(A^D\) be the Stokes Neumann operator and Stokes Dirichlet operator on \(\Omega \), respectively. We study the associated Stokes version of the Dirichlet-to-Neumann operator and show a Krein formula which relates these three Stokes version operators. We also prove a Stokes version of the Friedlander
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Bi-objective and hierarchical control for the Burgers equation J. Evol. Equ. (IF 1.4) Pub Date : 2024-03-15 F. D. Araruna, E. Fernández-Cara, L. C. da Silva
We present some results concerning the control of the Burgers equation. We analyze a bi-objective optimal control problem and then the hierarchical null controllability through a Stackelberg–Nash strategy, with one leader and two followers. The results may be viewed as an extension to this nonlinear setting of a previous analysis performed for linear and semilinear heat equations. They can also be
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Refined decay rates of $$C_0$$ -semigroups on Banach spaces J. Evol. Equ. (IF 1.4) Pub Date : 2024-03-15 Genilson Santana, Silas L. Carvalho
We study rates of decay for \(C_0\)-semigroups on Banach spaces under the assumption that the norm of the resolvent of the semigroup generator grows with \(|s|^{\beta }\log (|s|)^b\), \(\beta , b \ge 0\), as \(|s|\rightarrow \infty \), and with \(|s|^{-\alpha }\log (1/|s|)^a\), \(\alpha , a \ge 0\), as \(|s|\rightarrow 0\). Our results do not suppose that the semigroup is bounded. In particular, for
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Generic alignment conjecture for systems of Cucker–Smale type J. Evol. Equ. (IF 1.4) Pub Date : 2024-03-15 Roman Shvydkoy
The generic alignment conjecture states that for almost every initial data on the torus solutions to the Cucker–Smale system with a strictly local communication align to the common mean velocity. In this note, we present a partial resolution of this conjecture using a statistical mechanics approach. First, the conjecture holds in full for the sticky particle model representing, formally, infinitely
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Remarks on uniqueness and energy conservation for electron-MHD system J. Evol. Equ. (IF 1.4) Pub Date : 2024-03-15 Fan Wu
This paper is concerned with the uniqueness and energy conservation of weak solutions for Electron-MHD system. Under suitable assumptions, we first show that the Electron-MHD system has a unique weak solution. In addition, we show that weak solution conserves energy if \(\nabla \times b\in L^2(0, T; L^4({\mathbb {R}}^d))(d\ge 2)\) or \( \nabla \times b \in L^{\frac{4d+8}{d+4}}\left( 0, T; L^{\frac
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Strong solutions and attractor dimension for 2D NSE with dynamic boundary conditions J. Evol. Equ. (IF 1.4) Pub Date : 2024-03-15
Abstract We consider incompressible Navier–Stokes equations in a bounded 2D domain, complete with the so-called dynamic slip boundary conditions. Assuming that the data are regular, we show that weak solutions are strong. As an application, we provide an explicit upper bound of the fractal dimension of the global attractor in terms of the physical parameters. These estimates comply with analogous results
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On the separation property and the global attractor for the nonlocal Cahn-Hilliard equation in three dimensions J. Evol. Equ. (IF 1.4) Pub Date : 2024-03-15 Andrea Giorgini
We consider the nonlocal Cahn-Hilliard equation with constant mobility and singular potential in three dimensional bounded and smooth domains. This model describes phase separation in binary fluid mixtures. Given any global solution (whose existence and uniqueness are already known), we prove the so-called instantaneous and uniform separation property: any global solution with initial finite energy
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Stability estimates for semigroups in the Banach case J. Evol. Equ. (IF 1.4) Pub Date : 2024-03-15
Abstract The purpose of this paper is to revisit previous works of the author with Helffer and Sjöstrand (arXiv:1001.4171v1. 2010; Int Equ Op Theory 93(3):36, 2021) on the stability of semigroups which were proved in the Hilbert case by considering the Banach case at the light of a paper by Latushkin and Yurov (Discrete Contin Dyn Syst 33:5203–5216, 2013).
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Some aspects of the Floquet theory for the heat equation in a periodic domain J. Evol. Equ. (IF 1.4) Pub Date : 2024-03-15 Marcus Rosenberg, Jari Taskinen
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A perturbative approach to Hölder continuity of solutions to a nonlocal p-parabolic equation J. Evol. Equ. (IF 1.4) Pub Date : 2024-03-15 Alireza Tavakoli
We study local boundedness and Hölder continuity of a parabolic equation involving the fractional p-Laplacian of order s, with \(0
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Nonlinear partial differential equations on noncommutative Euclidean spaces J. Evol. Equ. (IF 1.4) Pub Date : 2024-02-26
Abstract Noncommutative Euclidean spaces—otherwise known as Moyal spaces or quantum Euclidean spaces—are a standard example of a non-compact noncommutative geometry. Recent progress in the harmonic analysis of these spaces gives us the opportunity to highlight some of their peculiar features. For example, the theory of nonlinear partial differential equations has unexpected properties in this noncommutative
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Well-posedness and longtime dynamics for the finitely degenerate parabolic and pseudo-parabolic equations J. Evol. Equ. (IF 1.4) Pub Date : 2024-02-26 Gongwei Liu, Shuying Tian
We consider the initial-boundary value problem for degenerate parabolic and pseudo-parabolic equations associated with Hörmander-type operator. Under the subcritical growth restrictions on the nonlinearity f(u), which are determined by the generalized Métivier index, we establish the global existence of solutions and the corresponding attractors. Finally, we show the upper semicontinuity of the attractors
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Homogeneous Sobolev global-in-time maximal regularity and related trace estimates J. Evol. Equ. (IF 1.4) Pub Date : 2024-02-12 Anatole Gaudin
In this paper, we prove global-in-time \(\dot{\textrm{H}}^{\alpha ,q}\)-maximal regularity for a class of injective, but not invertible, sectorial operators on a UMD Banach space X, provided \(q\in (1,+\infty )\), \(\alpha \in (-1+1/q,1/q)\). We also prove the corresponding trace estimate, so that the solution to the canonical abstract Cauchy problem is continuous with values in a not necessarily complete
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Existence of a weak solution and blow-up of strong solutions for a two-component Fornberg–Whitham system J. Evol. Equ. (IF 1.4) Pub Date : 2024-02-10 Zhihao Bai, Yang Wang, Long Wei
In this paper, we investigate the existence of a weak solution and blow-up of strong solutions to a two-component Fornberg–Whitham system. Due to the absence of some useful conservation laws, we establish the existence of a weak solution to the system in lower order Sobolev spaces \(H^{s}\times H^{s-1}\) (\(s\in (1,3/2]\)) via a modified pseudo-parabolic regularization method. And then, a blow-up scenario
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Pointwise space-time estimates of two-phase fluid model in dimension three J. Evol. Equ. (IF 1.4) Pub Date : 2024-02-10 Zhigang Wu, Wenyue Zhou
We studied the pointwise space-time behavior of the classical solution to the Cauchy problem of two-phase fluid model derived by Choi (SIAM J Math Anal 48:3090–3122, 2016) when the initial data is sufficiently small and regular. This model is the compressible damped Euler system coupled with the compressible Naiver–Stokes system via a drag force. As we know, Liu and Wang (Commun Math Phys 196:145–173
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Well-posedness and asynchronous exponential growth of an age-weighted structured fish population model with diffusion in $$L^1$$ J. Evol. Equ. (IF 1.4) Pub Date : 2024-02-10 Samir Boujijane, Said Boulite, Mohamed Halloumi, Lahcen Maniar, Abdelaziz Rhandi
In the present paper, we address the asymptotic behavior of a fish population system structured in age and weight, while also incorporating spatial effects. Initially, we develop an abstract perturbation result concerning the essential spectral radius, employing the regular systems approach. Following that, we present the model in the form of a perturbed boundary problem, which involves unbounded operators
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On a thermodynamically consistent model for magnetoviscoelastic fluids in 3D J. Evol. Equ. (IF 1.4) Pub Date : 2024-02-10 Hengrong Du, Yuanzhen Shao, Gieri Simonett
We introduce a system of equations that models a non-isothermal magnetoviscoelastic fluid. We show that the model is thermodynamically consistent, and that the critical points of the entropy functional with prescribed energy correspond exactly with the equilibria of the system. The system is investigated in the framework of quasilinear parabolic systems and shown to be locally well-posed in an \(L_p\)-setting
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Stability and optimal decay for the 3D magnetohydrodynamic equations with only horizontal dissipation J. Evol. Equ. (IF 1.4) Pub Date : 2024-02-10 Haifeng Shang, Jiahong Wu, Qian Zhang
This paper develops an effective approach to establishing the optimal decay estimates on solutions of the 3D anisotropic magnetohydrodynamic (MHD) equations with only horizontal dissipation. As our first step, we prove the global existence and stability of solutions to the aforementioned MHD system emanating from any initial data with small \(H^1\)-norm. Due to the lack of dissipation in the vertical
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Finite- and infinite-time cluster formation for alignment dynamics on the real line J. Evol. Equ. (IF 1.4) Pub Date : 2024-02-10 Trevor M. Leslie, Changhui Tan
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Long time behavior of solutions of an electroconvection model in $${\mathbb {R}}^2$$ J. Evol. Equ. (IF 1.4) Pub Date : 2024-02-10
Abstract We consider a two dimensional electroconvection model which consists of a nonlinear and nonlocal system coupling the evolutions of a charge distribution and a fluid. We show that the solutions decay in time in \(L^2({{\mathbb {R}}}^2)\) at the same sharp rate as the linear uncoupled system. This is achieved by proving that the difference between the nonlinear and linear evolution decays at
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Persistence and asymptotic analysis of solutions of nonlinear wave equations J. Evol. Equ. (IF 1.4) Pub Date : 2024-01-17 Igor Leite Freire
We consider persistence properties of solutions for a generalised wave equation including vibration in elastic rods and shallow water models, such as the BBM, the Dai’s, the Camassa–Holm, and the Dullin–Gottwald–Holm equations, as well as some recent shallow water equations with Coriolis effect. We establish unique continuation results and exhibit asymptotic profiles for the solutions of the general
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Orbital instability of periodic waves for scalar viscous balance laws J. Evol. Equ. (IF 1.4) Pub Date : 2024-01-17 Enrique Álvarez, Jaime Angulo Pava, Ramón G. Plaza
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Global well-posedness of the incompressible Hall-MHD system in critical spaces J. Evol. Equ. (IF 1.4) Pub Date : 2024-01-11 Mikihiro Fujii
In this paper, we consider the initial value problem of the incompressible Hall-MHD system and prove the global well-posedness in the scaling critical class \({\dot{B}}_{p,\infty }^{-1+\frac{3}{p}}(\mathbb {R}^3)\times ({\dot{B}}_{p,\infty }^{-1+\frac{3}{p}}(\mathbb {R}^3) \cap L^{\infty }(\mathbb {R}^3))\) for \(3< p < \infty \). Moreover, we also refine the smallness conditions and show that our
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Rate of convergence for reaction–diffusion equations with nonlinear Neumann boundary conditions and $${\mathcal {C}}^1$$ variation of the domain J. Evol. Equ. (IF 1.4) Pub Date : 2024-01-11 Marcone C. Pereira, Leonardo Pires
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A Kalman condition for the controllability of a coupled system of Stokes equations J. Evol. Equ. (IF 1.4) Pub Date : 2024-01-11 Takéo Takahashi, Luz de Teresa, Yingying Wu-Zhang
We consider the controllability of a class of systems of n Stokes equations, coupled through terms of order zero and controlled by m distributed controls. Our main result states that such a system is null-controllable if and only if a Kalman type condition is satisfied. This generalizes the case of finite-dimensional systems and the case of systems of coupled linear heat equations. The proof of the
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Gradient profile for the reconnection of vortex lines with the boundary in type-II superconductors J. Evol. Equ. (IF 1.4) Pub Date : 2023-12-18 Yi C. Huang, Hatem Zaag
In a recent work, Duong, Ghoul and Zaag determined the gradient profile for blowup solutions of standard semilinear heat equation with power nonlinearities in the (supposed to be) generic case. Their method refines the constructive techniques introduced by Bricmont and Kupiainen and further developed by Merle and Zaag. In this paper, we extend their refinement to the problem about the reconnection
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Weak and parabolic solutions of advection–diffusion equations with rough velocity field J. Evol. Equ. (IF 1.4) Pub Date : 2023-12-16 Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa
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Temporal regularity of the solution to the incompressible Euler equations in the end-point critical Triebel–Lizorkin space $$F^{d+1}_{1, \infty }(\mathbb {R}^d)$$ J. Evol. Equ. (IF 1.4) Pub Date : 2023-11-28 Hee Chul Pak
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On a quasilinear fully parabolic predator–prey model with indirect pursuit-evasion interaction J. Evol. Equ. (IF 1.4) Pub Date : 2023-11-28 Chuanjia Wan, Pan Zheng, Wenhai Shan
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Asymptotic behavior of solutions for nonlinear parabolic problems with Marcinkiewicz data J. Evol. Equ. (IF 1.4) Pub Date : 2023-11-28 Lucio Boccardo, Luigi Orsina, Maria Michaela Porzio
In this paper we prove the asymptotic behavior, as t tends to zero, of solutions of nonlinear parabolic equations with initial data belonging to Marcinkiewicz spaces. Namely, that if the initial datum \(u_{0}\) belongs to \(M^{m}(\Omega )\), then $$\begin{aligned} \Vert u(t)\Vert _{\scriptstyle L^{r}(\Omega )}^{*} \le {\mathcal {C}}\,\frac{\Vert u_{0}\Vert _{\scriptstyle L^{m}(\Omega )}^{*}}{t^{\frac{N}{2}\left(
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A pathwise regularization by noise phenomenon for the evolutionary p-Laplace equation J. Evol. Equ. (IF 1.4) Pub Date : 2023-11-09 Florian Bechtold, Jörn Wichmann
We study an evolutionary p-Laplace problem whose potential is subject to a translation in time. Provided the trajectory along which the potential is translated admits a sufficiently regular local time, we establish existence of solutions to the problem for singular potentials for which a priori bounds in classical approaches break down, thereby establishing a pathwise regularization by noise phenomena
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Boundedness of the conformal hyperboloidal energy for a wave-Klein–Gordon model J. Evol. Equ. (IF 1.4) Pub Date : 2023-11-09 Philippe G. LeFloch, Jesús Oliver, Yoshio Tsutsumi
We consider the global evolution problem for a model which couples together a nonlinear wave equation and a nonlinear Klein–Gordon equation, and was introduced by P.G. LeFloch and Y. Ma and, independently, by Q. Wang. By revisiting the Hyperboloidal Foliation Method, we establish that a weighted energy of the solutions remains (almost) bounded for all times. The new ingredient in the proof is a hierarchy
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Large time behavior of signed fractional porous media equations on bounded domains J. Evol. Equ. (IF 1.4) Pub Date : 2023-11-06 Giovanni Franzina, Bruno Volzone
Following the methodology of Brasco (Adv Math 394:108029, 2022), we study the long-time behavior for the signed fractional porous medium equation in open bounded sets with smooth boundary. Homogeneous exterior Dirichlet boundary conditions are considered. We prove that if the initial datum has sufficiently small energy, then the solution, once suitably rescaled, converges to a nontrivial constant sign
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An $$L^1$$ -theory for a nonlinear temporal periodic problem involving p(x)-growth structure with a strong dependence on gradients J. Evol. Equ. (IF 1.4) Pub Date : 2023-11-06 Abderrahim Charkaoui, Nour Eddine Alaa
We investigate the existence of a time-periodic solution to a nonlinear evolution equation involving p(x)-growth conditions with irregular data. We tackle our problem in a suitable functional setting by considering the so-called variable exponent Lebesgue and Sobolev spaces. By assuming that the data belongs only to \(L^1\), we prove the existence of a renormalized time-periodic solution to the studied
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The Willmore flow of Hopf-tori in the 3-sphere J. Evol. Equ. (IF 1.4) Pub Date : 2023-10-28 Ruben Jakob
In this article, the author investigates flow lines of the classical Willmore flow, which start to move in a smooth parametrization of a Hopf-torus in \(\textbf{S}^3\). We prove that any such flow line of the Willmore flow exists globally, in particular does not develop any singularities, and subconverges to some smooth Willmore-Hopf-torus in every \(C^{m}\)-norm. Moreover, if in addition the Willmore
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Optimal regularity for degenerate Kolmogorov equations in non-divergence form with rough-in-time coefficients J. Evol. Equ. (IF 1.4) Pub Date : 2023-10-26 Stefano Pagliarani, Giacomo Lucertini, Andrea Pascucci
We consider a class of degenerate equations in non-divergence form satisfying a parabolic Hörmander condition, with coefficients that are measurable in time and Hölder continuous in the space variables. By utilizing a generalized notion of strong solution, we establish the existence of a fundamental solution and its optimal Hölder regularity, as well as Gaussian estimates. These results are key to
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Moore Gibson Thompson thermoelastic plates: comparisons J. Evol. Equ. (IF 1.4) Pub Date : 2023-10-26 Hugo D. Fernández Sare, Ramón Quintanilla
In this paper we investigate two examples of thermoelastic plates free of the paradox of instantaneous propagation of thermal or mechanical waves when only one of them is dissipative and the other is conservative. To be precise we consider a Moore–Gibson–Thompson plate with type II heat conduction and a conservative elastic plate with Moore–Gibson–Thompson heat conduction. In both cases we prove the
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Critical exponents for the p-Laplace heat equations with combined nonlinearities J. Evol. Equ. (IF 1.4) Pub Date : 2023-10-26 Berikbol T. Torebek
This paper studies the large-time behavior of solutions to the quasilinear inhomogeneous parabolic equation with combined nonlinearities. This equation is a natural extension of the heat equations with combined nonlinearities considered by Jleli et al. (Proc Am Math Soc 148:2579–2593, 2020). Firstly, we focus on an interesting phenomenon of discontinuity of the critical exponents. In particular, we
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Well-posedness of the Kolmogorov two-equation model of turbulence in optimal Sobolev spaces J. Evol. Equ. (IF 1.4) Pub Date : 2023-10-24 Ophélie Cuvillier, Francesco Fanelli, Elena Salguero
In this paper, we study the well-posedness of the Kolmogorov two-equation model of turbulence in a periodic domain \(\mathbb {T}^d\), for space dimensions \(d=2,3\). We admit the average turbulent kinetic energy k to vanish in part of the domain, i.e. we consider the case \(k \ge 0\); in this situation, the parabolic structure of the equations becomes degenerate. For this system, we prove a local well-posedness
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Doubly nonlinear equations for the 1-Laplacian J. Evol. Equ. (IF 1.4) Pub Date : 2023-10-17 J. M. Mazón, A. Molino, J. Toledo
This paper is concerned with the Neumann problem for a class of doubly nonlinear equations for the 1-Laplacian, $$\begin{aligned} \frac{\partial v}{\partial t} - \Delta _1 u \ni 0 \hbox { in } (0, \infty ) \times \Omega , \quad v\in \gamma (u), \end{aligned}$$ and initial data in \(L^1(\Omega )\), where \(\Omega \) is a bounded smooth domain in \({\mathbb {R}}^N\) and \(\gamma \) is a maximal monotone
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Frequency theorem and inertial manifolds for neutral delay equations J. Evol. Equ. (IF 1.4) Pub Date : 2023-10-14 Mikhail Anikushin
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Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques J. Evol. Equ. (IF 1.4) Pub Date : 2023-10-06 Ning-An Lai, Nico Michele Schiavone
In this paper, we are interested in the upper bound of the lifespan estimate for the compressible Euler system with time-dependent damping and small initial perturbations. We employ some techniques from the blow-up study of nonlinear wave equations. The novelty consists in the introduction of tools from the Orlicz spaces theory to handle the nonlinear term emerging from the pressure \(p \equiv p(\rho
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Ill-posedness of the Cauchy problem for the $$\mu $$ -Camassa–Holm-type equations J. Evol. Equ. (IF 1.4) Pub Date : 2023-09-30 Kexin Yan, Hao Wang, Ying Fu
The \(\mu \)-Camassa–Holm equation and the modified \(\mu \)-Camassa–Holm equation, as the nonlocal counterparts of the Camassa–Holm and modified Camassa–Holm equations, are two integrable models. Local well-posedness of the Cauchy problems for the two equations has been established in the space \(C([0,T), H^s(\mathbb {S}))\bigcap C^1([0,T), H^{s-1}(\mathbb {S}))\), respectively, when \(s>3/2\) and
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Stability for a composite of Timoshenko laminated beams J. Evol. Equ. (IF 1.4) Pub Date : 2023-09-27 M. S. Alves, R. N. Monteiro
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On the admissibility of observation operators in the context of maximal regularity J. Evol. Equ. (IF 1.4) Pub Date : 2023-09-15 O. El Mennaoui, S. Hadd, Y. Kharou
We study admissible observation operators for perturbed evolution equations using the concept of maximal regularity. We first show the invariance of the maximal \(L^p\)-regularity under non-autonomous Miyadera–Voigt perturbations. Second, we establish the invariance of admissibility of observation operators under such a class of perturbations. Finally, we illustrate our result with two examples, one
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Modified scattering for the fractional mKdV equation J. Evol. Equ. (IF 1.4) Pub Date : 2023-08-21 Nakao Hayashi, Pavel I. Naumkin
We study the large-time asymptotics of solutions to the fractional modified Korteweg–de Vries equation $$\begin{aligned} \left\{ \begin{array}{c} \partial _{t}u+\frac{1}{\alpha }\left| \partial _{x}\right| ^{\alpha -1}\partial _{x}u=\partial _{x}\left( u^{3}\right) ,~ t>0,\ x\in {\mathbb {R}}\textbf{,} \\ u\left( 0,x\right) =u_{0}\left( x\right) ,\ x\in {\mathbb {R}}\textbf{,} \end{array} \right. \end{aligned}$$(0
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Weighted energy method for semilinear wave equations with time-dependent damping J. Evol. Equ. (IF 1.4) Pub Date : 2023-08-14 Motohiro Sobajima
Of concern is the energy decay property of solutions to wave equations with time-dependent damping. A reasonable class of damping coefficients for the framework of weighted energy methods is proposed, which contains not only the model of “effective” damping \((1+t)^{-\beta }\) \((-1\le \beta <1)\), but also non-differentiable functions with a suitable behavior at \(t\rightarrow \infty \). As an application
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Time-weighted estimates for the Blackstock equation in nonlinear ultrasonics J. Evol. Equ. (IF 1.4) Pub Date : 2023-08-05 Vanja Nikolić, Belkacem Said-Houari
High frequencies at which ultrasonic waves travel give rise to nonlinear phenomena. In thermoviscous fluids, these are captured by Blackstock’s acoustic wave equation with strong damping. We revisit in this work its well-posedness analysis. By exploiting the parabolic-like character of this equation due to strong dissipation, we construct a time-weighted energy framework for investigating its local
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Blow-up for a stochastic model of chemotaxis driven by conservative noise on $$\mathbb {R}^2$$ J. Evol. Equ. (IF 1.4) Pub Date : 2023-08-05 Avi Mayorcas, Milica Tomašević
We establish criteria on the chemotactic sensitivity \(\chi \) for the non-existence of global weak solutions (i.e., blow-up in finite time) to a stochastic Keller–Segel model with spatially inhomogeneous, conservative noise on \(\mathbb {R}^2\). We show that if \(\chi \) is sufficiently large then blow-up occurs with probability 1. In this regime, our criterion agrees with that of a deterministic
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On the existence and Hölder regularity of solutions to some nonlinear Cauchy–Neumann problems J. Evol. Equ. (IF 1.4) Pub Date : 2023-08-05 Alessandro Audrito
We prove uniform parabolic Hölder estimates of De Giorgi–Nash–Moser type for sequences of minimizers of the functionals $$\begin{aligned} {\mathcal {E}}_\varepsilon (W) = \int _0^\infty \frac{e^{- t/\varepsilon }}{\varepsilon } \bigg \{ \int _{\mathbb {R}_+^{N+1}} y^a \left( \varepsilon |\partial _t W|^2 + |\nabla W|^2 \right) \textrm{d}X + \int _{\mathbb {R}^N \times \{0\}} \Phi (w) \,\textrm{d}x\bigg
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An explicit time for the uniform null controllability of a linear Korteweg-de Vries equation J. Evol. Equ. (IF 1.4) Pub Date : 2023-07-25 Nicolás Carreño, Cristóbal Loyola
In this paper, we consider a linear Korteweg-de Vries equation posed in a bounded interval and study the time dependency with respect to the interval length and the transport coefficient, for which the uniform null controllability holds as the dispersion coefficient goes to zero. We consider two cases of boundary controls. First, only one control on the left end of the interval, and then, two controls
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A singular perturbation problem for mean field games of acceleration: application to mean field games of control J. Evol. Equ. (IF 1.4) Pub Date : 2023-07-26 Cristian Mendico
The singular perturbation of mean field game systems arising from minimization problems with control of acceleration is addressed, that is, we analyze the behavior of solutions as the acceleration costs vanishes. In this setting, the Hamiltonian fails to be strictly convex and coercive w.r.t. the momentum variable and, so, the classical results for Tonelli Hamiltonian systems cannot be applied. However
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Singular integral equations with applications to travelling waves for doubly nonlinear diffusion J. Evol. Equ. (IF 1.4) Pub Date : 2023-07-24 Alejandro Gárriz
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Higher Hölder regularity for nonlocal parabolic equations with irregular kernels J. Evol. Equ. (IF 1.4) Pub Date : 2023-07-11 Sun-Sig Byun, Hyojin Kim, Kyeongbae Kim
We study a nonlocal parabolic equation with an irregular kernel coefficient to establish higher Hölder regularity under an appropriate higher integrablilty on the nonhomogeneous terms and a minimal regularity assumption on the kernel coefficient.
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On well-posedness for some Korteweg–de Vries type equations with variable coefficients J. Evol. Equ. (IF 1.4) Pub Date : 2023-07-07 Luc Molinet, Raafat Talhouk, Ibtissame Zaiter
In this paper, KdV-type equations with time- and space-dependent coefficients are considered. Assuming that the dispersion coefficient in front of \( u_{xxx} \) is positive and uniformly bounded away from zero and that a primitive function of the ratio between the anti-dissipation and the dispersion coefficients is bounded from below, we prove the existence and uniqueness of a solution u such that
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Quantified hydrodynamic limits for Schrödinger-type equations without the nonlinear potential J. Evol. Equ. (IF 1.4) Pub Date : 2023-07-06 Jeongho Kim, Bora Moon
We establish rigorous and quantified hydrodynamic limits of the Schrödinger-type equations. Precisely, we consider the Schrödinger equation, Hartree equation, and Chern–Simons–Schrödinger equations and identify the hydrodynamic equations of them, when the Planck constant is negligible. In particular, we focus on the case when there is no Gross–Pitaevskii type self-interacting potential. In this situation
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Conservation laws and Hamilton–Jacobi equations with space inhomogeneity J. Evol. Equ. (IF 1.4) Pub Date : 2023-07-01 Rinaldo M. Colombo, Vincent Perrollaz, Abraham Sylla