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

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 795-812, January 2021. This paper is concerned with the existence of compactly supported admissible solutions to the Cauchy problem for the isentropic compressible Euler equations. In more than one space dimension, convex integration techniques developed by De Lellis and Székelyhidi and by Chiodaroli enable us to prove failure of uniqueness

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 754-794, January 2021. This paper deals with a two-phase fluid free boundary problem in a slot-film cooling. We give two well-posedness results on the existence and uniqueness of the incompressible inviscid two-phase fluid with a jump relation on a free interface. The problem formulates the oblique injection of an incompressible ideal

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 730-753, January 2021. The Anderson--Witting model is a relativistic generalization of the Bhatnagar--Gross--Krook model which is well-known as the relaxation-time approximation of the celebrated Boltzmann equation. In this paper, we address the stationary boundary value problems to the Anderson--Witting model in slab geometry. We prove

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 710-729, January 2021. In this paper, we address the problem of maximizing the Steklov eigenvalues with a diameter constraint. We provide an estimate of the Steklov eigenvalues for a convex domain in terms of its diameter and volume, and we show the existence of an optimal convex domain. We establish that balls are never maximizers, even

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 681-709, January 2021. We consider a large class of interacting particle systems in one dimension described by an energy whose interaction potential is singular and nonlocal. This class covers Riesz gases (in particular, log gases) and applications to plasticity and approximation theory of functions. While it is well established that the

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 649-680, January 2021. We develop an existence and regularity theory for a class of degenerate one-phase free boundary problems. In this way we unify the basic theories in free boundary problems like the classical one-phase problem, the obstacle problem, or more generally for minimizers of the Alt--Phillips functional.

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 574-648, January 2021. Consider the dynamics of a layer of viscous incompressible fluid under the influence of gravity. The upper boundary is a free boundary with the effect of surface tension taken into account, and the lower boundary is a fixed boundary on which the Navier slip condition is imposed. It is proved that there is a uniform

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 530-573, January 2021. In this article, we consider the hyperbolic Ericksen--Leslie system for incompressible liquid crystals without kinematic transport in three spatial dimensions, which is a nonlinear coupling of incompressible Navier--Stokes equations with wave map to $\mathbb{S}^2$. Global regularity for small and smooth initial data

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 509-529, January 2021. This article is about hyperelastic deformations of plates (planar domains) which minimize a neohookean-type energy. Particularly, we investigate a stored energy functional introduced by J. M. Ball [Proc. Roy. Soc. Edinb. Sect. A, 88 (1981), pp. 315--328]. The mappings under consideration are Sobolev homeomorphisms

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 491-508, January 2021. We compute the lamination convex hull of the stationary incompressible porous media (IPM) equations. We also show in bounded domains that for subsolutions of stationary IPM taking values in the lamination convex hull, velocity vanishes identically and density depends only on height. We relate the results to the infinite

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 453-490, January 2021. A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model introduced here is characterized by an energy with two contributions, the surface and the elastic-bulk energy, and it is formally justified starting

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 435-452, January 2021. We study a class of fractional parabolic equations involving a time-dependent magnetic potential and formulate the corresponding inverse problem. We determine both the magnetic potential and the electric potential from the exterior partial measurements of the Dirichlet-to-Neumann map.

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 386-434, January 2021. We study the reducibility of a linear Schrodinger equation subject to a small unbounded almost periodic perturbation which is analytic in time and space. Under appropriate assumptions on the smallness, analyticity, and on the frequency of the almost periodic perturbation, we prove that such an equation is reducible

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 351-385, January 2021. We provide explicit examples to show that the relaxation of functionals $L^p(\Omega;{\mathbb{R}}^m) \ni u\mapsto \int_\Omega\int_\Omega W(u(x), u(y))\, dx\, dy$, where $\Omega\subset{\mathbb{R}}^n$ is an open and bounded set, $1

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 323-350, January 2021. We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if the diffusion coefficients are close to each other, or if the diffusion coefficients

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 309-322, January 2021. The goal of this paper is to derive rigorously macroscopic traffic flow models from microscopic models. More precisely, for the microscopic models, we consider follow-the-leader type models with different types of drivers and vehicles which are distributed randomly on the road. After a rescaling, we show that the

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 279-308, January 2021. In this paper, we prove the structural stability of the transonic shocks for three-dimensional axisymmetric Euler system with swirl velocity under the perturbations for the incoming supersonic flow, the nozzle boundary, and the exit pressure. Compared with the known results on the stability of transonic shocks, one

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 253-278, January 2021. We prove a new decomposition result for rank $m$ symmetric tensor fields which generalizes the well-known solenoidal and potential decomposition of tensor fields. This decomposition is then used to describe the kernel and prove an injectivity result for the first $(k+1)$ integral moment transforms of symmetric $m$-tensor

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 221-252, January 2021. We study linear and quasilinear Venttsel boundary value problems involving elliptic operators with discontinuous coefficients. On the basis of the a priori estimates obtained, maximal regularity and strong solvability in Sobolev spaces are proved.

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 181-220, January 2021. We consider Coulomb gas models for which the empirical measure typically concentrates, when the number of particles becomes large, on an equilibrium measure minimizing an electrostatic energy. We study the behavior when the gas is conditioned on a rare event. We first show that the special case of quadratic confinement

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 133-180, January 2021. In this paper, we are concerned with the global existence and stability of a smooth supersonic Euler flow with vacuum state at infinity in a three-dimensional (3-D) infinitely long divergent nozzle. The flow is described by 3-D compressible steady Euler equations, which are quasilinear multidimensional hyperbolic

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 111-132, January 2021. The paper is mainly concerned with an approximate three-ball inequality for solutions in elliptic periodic homogenization. We consider a family of second order operators $\mathcal{L}_\epsilon$ in divergence form with rapidly oscillating and periodic coefficients. It is the first time such an approximate three-ball

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 62-110, January 2021. We study the barycenter of the Hellinger--Kantorovich metric over nonnegative measures on compact, convex subsets of $\mathbb{R}^d$. The article establishes existence, uniqueness (under suitable assumptions), and equivalence between a coupled-two-marginal and a multimarginal formulation. We analyze the HK barycenter

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 32-61, January 2021. In this paper we establish an averaging principle for the complex Ginzburg--Landau equations, perturbed by a mixing random force. The principle applies to study the limiting behavior of solutions for the equations on long time intervals, as well as the limiting behavior of their stationary measures. Next we apply this

SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 1-31, January 2021. The Onsager--Machlup (OM) and Freidlin--Wentzell (FW) functionals are both widely used in seeking the most probable transition path between two states for a diffusion process. We study the relation between these two functionals on the space of curves. We prove that the $\Gamma$-limit of the OM functional on the space

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6412-6441, January 2020. A recent problem of interest in inverse problems has been the study of eigenvalue problems arising from scattering theory and their potential use as target signatures in nondestructive testing of materials. Toward this pursuit we introduce a new eigenvalue problem related to Maxwell's equations that is generated

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6379-6411, January 2020. We obtain sharp decay estimates and asymptotics for small solutions to the one-dimensional Klein--Gordon equation with constant coefficient cubic and spatially localized, variable coefficient cubic nonlinearities. Vector-field techniques to deal with the long-range nature of the cubic nonlinearity become problematic

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6338-6378, January 2020. In this work, we study a system coupling the incompressible Navier--Stokes equations in a cylindrical type domain with an elastic structure, governed by a damped shell equation, located at the lateral boundary of the domain occupied by the fluid. We prove the existence of a unique maximal strong solution.

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6313-6337, January 2020. In this paper, we consider the compressible fluid model of Korteweg type which can be used as a phase transition model. It is shown that the system admits a unique, global strong solution for small initial data in ${\Bbb R}^N$, $3\leq N \leq 7$. In this study, the main tools are the maximal $L_p$-$L_q$ regularity

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6297-6312, January 2020. In this paper, we analyze a class of reaction-diffusion systems with delay and a Neumann condition from the dynamical behavior of the map that determines the equilibria. For scalar equations, a similar analysis was given by Yi and Zou in [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 466 (2010), pp. 2955--2973]

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6281-6296, January 2020. In this paper, we investigate discrete logarithmic energy problems in the unit circle. We study the equilibrium configuration of $n$ electrons and $n-1$ pairs of external protons of charge $+1/2$. It is shown that all the critical points of the discrete logarithmic energy are global minima, and they are the solutions

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6260-6280, January 2020. We introduce a PDE problem modeling a solidification/melting process in bounded two- or three-dimensional domains, coupling a phase-field equation and a Navier--Stokes--Boussinesq system, where the latent heat effect is considered via a modification of the Caginalp model. Moreover, the convection in the nonsolid

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6234-6259, January 2020. The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far, the method has not been proven to be able to handle extreme inclusions that correspond to some parts of the studied domain becoming either

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6222-6233, January 2020. We give a short and self-contained proof for rates of convergence of the Allen--Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter exists and starting from well-prepared initial data. Our approach is based on a relative entropy technique. In particular, it does

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6180-6221, January 2020. We prove the existence and asymptotic expansion of a large class of solutions to nonlinear Helmholtz equations of the form $(\Delta - \lambda^2) u = N[u]$, where $\Delta = -\sum_j \partial^2_j$ is the Laplacian on $\mathbb{R}^n$, $\lambda$ is a positive real number, and $N[u]$ is a nonlinear operator depending

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6155-6179, January 2020. We consider a nonlocal version of the quasi-static Navier--Stokes--Korteweg equations with a nonmonotone pressure law. This system governs the low-Reynolds number dynamics of a compressible viscous fluid that may take either a liquid or a vapor state. For a porous domain that is perforated by cavities with diameter

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6140-6154, January 2020. This paper considers the time-harmonic Maxwell's equations with anisotropic complex coefficients in a bounded Lipschitz domain. We first establish the $W^{1,r}$ estimates for divergence form equations with the coefficients being the small complex perturbations of real symmetric matrices in Lipschitz domains. As

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6105-6139, January 2020. We investigate the low Mach number limit for the three-dimensional quantum Navier--Stokes system. For general ill-prepared initial data, we prove strong convergence of finite energy weak solutions to weak solutions of the incompressible Navier--Stokes equations. Our approach relies on a quite accurate dispersive

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 6033-6104, January 2020. This paper is devoted to the study of the stability of the steady normal shock structure in potential flows under an unsteady perturbation. The dynamic stability problem is formulated as the well-posedness problem of an initial boundary value problem of a nonlinear wave equation in a cornered space domain with

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5994-6032, January 2020. In this paper, we deal with the relativistic Boltzmann equation in the whole space ${\mathbb{R}}_{x}^{3}$ under the closed to equilibrium setting. We obtain the existence, uniqueness, and large time behavior of the solution without imposing any Sobolev regularity (both the spatial and velocity variables) on the

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5892-5993, January 2020. We study the long-time asymptotic behavior of the solution $q(x,t) $, $x\in\mathbb{R}$, $t\in\mathbb{R}^+$, of the modified Korteweg--de Vries equation (MKdV) $q_t+6q^2q_x+q_{xxx}=0$ with step-like initial datum $\scriptsize q(x,0)\to \Big\{\begin{array}{@{}l@{}l@{}} c_-\quad& {for $x\to-\infty$},\\ c_+\quad& {for

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5865-5891, January 2020. We study the system $ (*) \Big\{\!\!\begin{array}{c} u_t = D_1 \Delta u - \chi_1 \nabla \cdot (u \nabla v) + u(\lambda_1 - \mu_1 u + a_1 v) \\ v_t = D_2 \Delta v + \chi_2 \nabla \cdot (v \nabla u) + v(\lambda_2 - \mu_2 v - a_2 u) \end{array} $ (inter alia) for $D_1, D_2, \chi_1, \chi_2, \lambda_1, \lambda_2, \mu_1

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5840-5864, January 2020. We consider a parabolic-parabolic Keller--Segel system in a ball of $ \mathbb{R}^N $ under the Neumann boundary condition. This was introduced as a model of aggregation of bacteria. The aggregation is mathematically defined as finite-time blowup. When $ N = 2 $, an optimal criterion for finite-time blowup was obtained

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5792-5839, January 2020. We introduce a new class of models for emergent dynamics. It is based on a new communication protocol which incorporates two main features: short-range kernels which restrict the communication to local metric balls, and anisotropic communication kernels, adapted to the local density in these balls, which form topological

SIAM Journal on Mathematical Analysis, Volume 52, Issue 6, Page 5775-5791, January 2020. In the present paper we extend the $L^2$ Korn interpolation and second inequalities in thin domains, proven in [D. Harutyunyan, SIAM J. Math. Anal., 50 (2018), pp. 4964--4982], to the space $L^p$ for any $1