SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 2691-2717, January 2021. We consider the time-harmonic Maxwell's equations with physical parameters, namely, the electric permittivity and the magnetic permeability, that are complex, possibly non-Hermitian, tensor fields. Both tensor fields verify a general ellipticity condition. In this work, the well-posedness of formulations for the

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2660-2689, January 2021. We deal with an inverse elastic scattering problem for the shape determination of a rigid scatterer in the time-harmonic regime. We prove a local stability estimate of $log\,log$ type for the identification of a scatterer by a single far-field measurement. The needed a priori condition on the closeness of the scatterers

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2631-2659, January 2021. We study a Paveri-Fontana type model, which describes the evolution of the mesoscopic distribution of vehicles through a combined effect of adjustment of the velocity with respect to nearby vehicles, and slowing down and speeding up of the vehicles arising as a result of exchange of velocity with the vehicles on

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2595-2630, January 2021. We consider the three-dimensional incompressible free-boundary magnetohydrodynamics (MHD) equations in a bounded domain with surface tension on the boundary. We establish an priori estimate for solutions in the Lagrangian coordinates with $H^{3.5}$ regularity. To the best of our knowledge, this is the first result

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2567-2594, January 2021. We consider the motion of the interface between two inviscid, incompressible, and dielectric fluids with different densities and permittivities, in the presence of a uniform electric field acting in a direction parallel to the undisturbed configuration. The system is assumed to be irrotational except the interface

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2523-2566, January 2021. In a classical survey [Mathematics in Industrial Problems, Springer-Verlag, New York, 1989, Chapter 16.2], Friedman proposed an open problem on the collision of two incompressible jets emerging from two axially symmetric nozzles. In this paper, we are concerned with the mathematical theory on this collision problem

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2491-2522, January 2021. We rigorously show the nonequilibrium-diffusion limit of the compressible Euler-P1 approximation model arising in radiation hydrodynamics as the Mach number tends to zero when the initial data is well prepared. In particular, the effect of the large temperature variation upon the limit is taken into account. The

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2476-2490, January 2021. Recently, the higher order averaging method for studying periodic solutions of both Lipschitz differential equations and discontinuous piecewise smooth differential equations was developed in terms of the Brouwer degree theory. Between the Lipschitz and the discontinuous piecewise smooth differential equations

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2452-2475, January 2021. We show propagation of moments in velocity for the three-dimensional Vlasov--Poisson system with a uniform magnetic field $B=(0,0,\omega)$ by adapting the work of Lions and Perthame. The added magnetic field also produces singularities at times which are the multiples of the cyclotron period $t=\frac{2\pi k}{\omega}$

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2427-2451, January 2021. We study the problem of recovering the initial data ($f, 0$) of the standard wave equation from the Neumann trace (the normal derivative) of the solution on the boundary of convex domains in arbitrary spatial dimension. Among others, this problem is relevant for tomographic image reconstruction including photoacoustic

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2373-2426, January 2021. It is shown that in core-radius cutoff regularized simplified elasticity (where the elastic energy depends quadratically on the full displacement gradient rather than its symmetrized version), the force on a dislocation curve by the negative gradient of the elastic energy asymptotically approaches the mean curvature

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2349-2372, January 2021. We study a stationary scattering problem related to the nonlinear Helmholtz equation $ - \Delta u -k^2 u = f(x,u) \ \ \text{in $\mathbbR^N$,} $ where $N \ge 3$ and $k>0$. For a given incident free wave $\phi\in L^\infty({\mathbb{R}}^N)$, we prove the existence of complex-valued solutions of the form $u=\varphi+u_{\text{sc}}$

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2319-2348, January 2021. We study master equations of the form $(\partial_t+L)^su=f\ {in}~\mathbb{R}\times\Omega,$ where $L$ is a divergence form elliptic operator and $\Omega\subseteq\mathbb{R}^n$. These are nonlocal equations of order $2s$ in space and $s$ in time that take into account the values of $u$ everywhere in $\Omega$ and for

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2275-2318, January 2021. We propose and analyze a finite-difference discretization of the Ambrosio--Tortorelli functional. It is known that if the discretization is made with respect to an underlying periodic lattice of spacing $\delta$, the discretized functionals $\Gamma$-converge to the Mumford--Shah functional only if $\delta\ll\varepsilon$

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2243-2274, January 2021. In this paper, we prove the global well-posedness for the focusing, cubic nonlinear Schrödinger equation on the product space $\mathbb{R} \times \mathbb{T}^3$ with initial data below the threshold that arises from the the ground state in the Euclidean setting. The defocusing analogue was discussed and proved in

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2206-2242, January 2021. We study nonlinear stability of pulled fronts in scalar parabolic equations on the real line of arbitrary order, under conceptual assumptions on existence and spectral stability of fronts. In this general setting, we establish sharp algebraic decay rates and temporal asymptotics of perturbations to the front. Some

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2134-2205, January 2021. The paper considers three-dimensional (3D) traveling surface waves on water of finite depth under the forces of gravity and surface tension using the exact governing equations, also called Euler equations. It was known that when two nondimensional constants $b$ and $\lambda$, which are related to the surface tension

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2084-2133, January 2021. Suppose that $\{u(t\,, x)\}_{t >0, x \in{\mathbb{R}}^d}$ is the solution to a $d$-dimensional parabolic Anderson model with delta initial condition and driven by a Gaussian noise that is white in time and has a spatially homogeneous covariance given by a nonnegative-definite measure $f$ which satisfies Dalang's

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 2027-2083, January 2021. The Patlak--Keller--Segel model can be used to model the nonlocal aggregation phenomena in the collective motion of cells or the evolution of the density of bacteria by chemotaxis. We consider the free boundary value problem for the Patlak--Keller--Segel model with homogeneous nonlinear degenerate diffusion in

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1993-2026, January 2021. We establish existence of solutions in a scale of classes weaker than the finite energy Leray class and stronger than the infinite energy Lemarié-Rieusset class. The new classes are based on the $L^2$ Wiener amalgam spaces. Solutions in the classes closer to the Leray class are shown to satisfy some properties

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1958-1992, January 2021. The present paper is devoted to the study of convergence of solutions of a Fokker--Planck equation (FPE) associated to a periodic stochastic differential equation with less regular coefficients under various Lyapunov conditions. In the case of nondegenerate noises, we prove two types of convergence of solutions

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1944-1957, January 2021. We prove an observability inequality from two time points for the linear KdV equation with an explicit constant. The proof relies on a quantitative analytic estimate for the linear KdV with compact support initial data and an uncertainty principle of super-analytic functions. Moreover, we obtain similar unique

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1908-1943, January 2021. This article deals with the regularity aspects of entropy solutions to scalar conservation laws. We show that for each $C^2$ flux in multiple dimensions (multi-D), there exists an entropy solution which does not belong to $BV_{loc}(\mathbb{R}^d)$ for all time. For this purpose, we construct a non-$BV_{loc}$ solution

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1886-1907, January 2021. The bitemperature Euler model describes a crucial step of inertial confinement fusion (ICF) when the plasma is quasineutral while ionic and electronic temperatures remain distinct. The model is written as a first-order hyperbolic system in nonconservative form with partially dissipative source terms. We consider

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1857-1885, January 2021. This paper is concerned with the variational problem for the elastic energy defined on symmetric graphs under the unilateral constraint. Assuming that the obstacle function satisfies the symmetric cone condition, we prove (i) uniqueness of minimizers and (ii) loss of regularity of minimizers and give (iii) complete

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1831-1856, January 2021. We give a sufficient condition for exponential stability of a network of lossless telegrapher's equations, coupled by linear time-varying boundary conditions. The sufficient conditions is in terms of dissipativity of the couplings, which is natural, for instance, in the context of microwave circuits. Exponential

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1818-1830, January 2021. In this paper, we introduce a new effective velocity to study the nonlinear stability of viscous shock waves to the one-dimensional system of viscoelasticity. Any viscous shock wave of arbitrary amplitudes to the system of viscoelasticity with nonstrictly convex constitutive relations is proved to be nonlinear

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1785-1817, January 2021. We consider a homogenization problem associated with quasi-crystalline multiple integrals of the form $u_\varepsilon\in L^p(\Omega;\mathbbm{R}^d) \mapsto \int_\Omega f_R(x,\frac{x}{\varepsilon}, u_\varepsilon(x)), dx,$ where \(u_ǎrepsilon) is subject to constant-coefficient linear partial differential constraints

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1745-1784, January 2021. In a three-dimensional bounded possibly multiply connected domain, we prove the existence, uniqueness, and regularity of some vector potentials, associated with a divergence-free function and satisfying mixed boundary conditions. For such a construction, the fundamental tool is the characterization of the kernel

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1711-1744, January 2021. We consider a compressible flow-structure interaction (FSI) PDE system which is linearized about some reference rest state. The deformable interface is under the effect of an ambient field generated by the underlying and unbounded material derivative term which further contributes to the nondissipativity of the

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1670-1710, January 2021. We are interested in the study of Blaschke--Santaló diagrams describing the possible inequalities involving the first Dirichlet eigenvalue, the perimeter, and the volume for different classes of sets. We give a complete description of the diagram for the class of open sets in $\mathbb{R}^d$, basically showing that

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1630-1669, January 2021. We consider the conductivity transmission problem in two dimensions with a simply connected inclusion of arbitrary shape. It is well known that the solvability of the transmission problem can be established via the boundary integral formulation in which the Neumann--Poincaré (NP) operator is involved. In this paper

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1579-1629, January 2021. We are concerned with the sonic-supersonic structures extracted from the transonic flow problems in gas dynamics. A local classical supersonic solution for the two-dimensional steady full Euler equations is established in an angular region bounded by the sonic curve and the characteristic curve. In order to overcome

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1546-1578, January 2021. The ensemble Kalman sampler (EKS) is a method introduced in [Garbuno-Inigo et al., SIAM J. Appl. Dyn. Syst., 19 (2020), pp. 412--441] to find approximately independent and identically distributed samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. The

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1509-1545, January 2021. We present some results of geometric convergence of level sets for solutions of total variation denoising as the regularization parameter tends to zero. The common feature among them is that they make use of explicit constructions of variational mean curvatures for general sets of finite perimeter. Consequently

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1492-1508, January 2021. In this paper, we consider an acoustic wave transmission problem with mixed boundary conditions of Dirichlet, Neumann, and impedance type. We will derive a formulation as a direct, space-time retarded boundary integral equation, where both Cauchy data are kept as unknowns on the impedance part of the boundary.

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1474-1491, January 2021. The electrostatic potentials $\phi$ associated with neutral periodic crystals are defined by lattice sums that are never absolutely convergent. The sum depends on the order of summation. The mean zero periodic solution of Poisson's equation, denoted ${\underline \phi}$, is a natural potential. So is the potential

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1434-1473, January 2021. This paper is concerned with the time-asymptotic behavior of strong solutions to the initial-boundary value problem of the isothermal compressible fluid models of Korteweg type with density-dependent viscosity and capillarity on the half-line $\mathbb{R}^+$. The case when the pressure $p(v)=v^{-\gamma}$, the viscosity

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1411-1433, January 2021. A three-component reaction-diffusion system is considered which originates from an extension of the classical May--Nowak model for viral infections to situations in which spatially heterogeneous dynamics need to be accounted for. In accordance with recent developments in the modeling literature, a particular focus

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1379-1410, January 2021. In this paper, we are mainly concerned with the physically interesting static Schrödinger--Hartree--Maxwell type equations $(-\Delta)^{s}u(x)=(\frac{1}{|x|^{\sigma}}\ast |u|^{p})u^{q}(x) \,\,\ {in} \,\,\, \mathbb{R}^{n}$ involving higher-order or higher-order fractional Laplacians, where $n\geq1$, $0

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1357-1378, January 2021. This paper studies convergence to equilibrium for the spatially inhomogeneous linear relaxation Boltzmann equation in Boltzmann entropy and related entropy functionals, the $p$-entropies. Villani [Hypocoercivity, in Memoirs of the American Mathematical Society, Vol. 202, American Mathematical Society, Providence

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1320-1356, January 2021. We prove that viscosity solutions of Hamilton--Jacobi--Bellman (HJB) equations, corresponding either to deterministic optimal control problems for systems of $n$ particles or to stochastic optimal control problems for systems of $n$ particles with a common noise, converge locally uniformly to the viscosity solution

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1295-1319, January 2021. We define a random step size tug-of-war game and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the gradient of the corresponding $p$-harmonic function. Moreover, we establish an improved Lipschitz

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1263-1294, January 2021. This is a continuation and an extension of our recent work [J. Math. Pures Appl., 143 (2020), pp. 116--161] on the geometric structures of Laplacian eigenfunctions and their applications to inverse scattering problems. In that work, we studied the analytic behavior of the Laplacian eigenfunctions at a point where

SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1239-1262, January 2021. The smoothed particle hydrodynamics (SPH) method is a popular, kernel-based discretization method for fluid-flow problems. Despite its frequent use, mathematical understanding is still limited. In [T. Franz and H. Wendland, SIAM J. Math. Anal., 50 (2018), pp. 4752--4784] we proved convergence for a specific flow

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 1214-1238, January 2021. The amplification of an external signal is a key step in direction sensing of biological cells. We consider a simple model for the response to a time-depending signal, which was previously proposed by the last three authors. The model consists of a bulk-surface reaction-diffusion model. We prove that in a suitable

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 1191-1213, January 2021. A PDE system consisting of the mechanical equilibrium and mass balance equations for displacement and capillary pressure as a model for fluid diffusion in a partially saturated viscoelastoplastic porous solid with a nonlinear solid-liquid interaction and a degenerate pressure-saturation function is shown to admit

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 1168-1190, January 2021. We establish a sharp estimate for a minimal number of binary digits (bits) needed to represent all bounded total generalized variation functions taking values in a general totally bounded metric space $(E,\rho)$ up to an accuracy of $\varepsilon>0$ with respect to the ${\bf L}^1$-distance. Such an estimate is explicitly

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 1122-1167, January 2021. We prove the existence and uniqueness of smooth solutions with large initial data for a system of equations modeling the interaction of short waves, governed by a nonlinear Schrödinger equation, and long waves, described by the equations of magnetohydrodynamics. In the model, the short waves propagate along the

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 1088-1121, January 2021. We consider elliptic equations of Schrödinger type with a right-hand side fixed and with the linear part of order zero given by a potential $V$. The main goal is to study the optimization problem for an integral cost depending on the solution $u_V$, when $V$ varies in a suitable class of admissible potentials.

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 1070-1087, January 2021. We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of the pressure in the deformed configuration. We also provide a convex relaxation

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 1049-1069, January 2021. We consider an inverse problem for the Boltzmann equation with nonlinear collision operator in dimensions $n\geq 2$. We show that the kinetic collision kernel can be uniquely determined from the incoming-to-outgoing mappings on the boundary of the domain provided that the kernel satisfies a monotonicity condition

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 1029-1048, January 2021. We show that the limit infimum, as time $\,t\,$ goes to infinity, of any uniformly bounded in time $H^{3/2+}\cap L^1$ solution to the intermediate long wave (ILW) equation converges to zero locally in an increasing-in-time region of space of order $\,t/\log(t)$. Also, for solutions with a mild $L^1$-norm growth

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 1004-1028, January 2021. We prove the existence of $m$-armed spiral wave solutions for the complex Ginzburg--Landau equation in the circular and spherical geometries. We establish a new global bifurcation approach and generalize the results of existence for rigidly rotating spiral waves. Moreover, we prove the existence of two new patterns:

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 973-1003, January 2021. In recent years, a lot of attention has been drawn to the question of whether logistic kinetics is sufficient to enforce the global existence of classical solutions or to prevent finite-time blow-up in various chemotaxis models. However, for several important chemotaxis models, only in the space two dimensional

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 937-972, January 2021. We study a population of $N$ particles, which evolve according to a diffusion process and interact through a dynamical network. In turn, the evolution of the network is coupled to the particles' positions. In contrast with the mean-field regime, in which each particle interacts with every other particle, i.e., with

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 914-936, January 2021. We prove a high-dimensional version of the Strichartz estimates for the unitary group associated to the free Zakharov--Kuznetsov equation. As a by-product, we deduce maximal estimates which allow us to prove local well-posedness for the generalized Zakharov--Kuznetsov equation in the whole subcritical case whenever

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 888-913, January 2021. In this paper, we establish the discreteness of transmission eigenvalues for Maxwell's equations. More precisely, we show that the spectrum of the transmission eigenvalue problem is discrete if the electromagnetic parameters $\varepsilon, \, \mu, \, \hat \varepsilon, \, \hat \mu$ in the equations characterizing the

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 855-887, January 2021. We construct one-parameter families of nonperiodic embedded minimal surfaces of infinite genus in $T \times \mathbb{R}$, where $T$ denotes a flat 2-tori. Each of our families converges to a foliation of $T \times \mathbb{R}$ by $T$. These surfaces then lift to minimal surfaces in $\mathbb{R}^3$ that are periodic

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 813-854, January 2021. In this article we are interested in quantitative homogenization results for linear elliptic equations in the nonstationary situation of a straight interface between two heterogeneous media. This extends previous work [M. Josien, Comm. Partial Differential Equations, 14 (2019), pp. 907--939] to a substantially more