SIAM Journal on Mathematical Analysis

We consider the generalized Radon transform (defined in terms of smooth weight functions) on hyperplanes in ${{\mathbb R}^n}$. We analyze general filtered backprojection type reconstruction methods for limited data with filters given by general ...

In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and a relaxed condition on the ...

In this paper, we consider the long wavelength limit for the quantum Euler--Poisson equation. Under the Gardner--Morikawa transform, we derive the quantum Korteweg--de Vries (KdV) equation by a reductive perturbation method. We show that the KdV dynamics ...

In this paper we extend Sylvester's approach via upper triangular compact operators to establish the discreteness of transmission eigenvalues for higher-order main terms and higher-order perturbations. The coefficients of the perturbations must be ...

We characterize the class of probability measures possessing finite moments of an arbitrary positive order in terms of the symmetric difference operators of their Fourier transforms. As an application, we prove the continuity of probability densities ...

This paper concerns properties of sonic curves for two-dimensional smooth subsonic-sonic and transonic steady potential flows, which are governed by quasi-linear degenerate elliptic equations and elliptic-hyperbolic mixed-type equations with degenerate free ...

The Kompaneets equation describes a field of photons exchanging energy by Compton scattering with the free electrons of a homogeneous, isotropic, nonrelativistic, thermal plasma. This paper strives to advance our understanding of how this equation captures ...

We study the regularity of Radon measures $\mu$ which satisfy that there exists a function $h_{\mu}$ in $H^1$, stationary harmonic such that $\Delta h_{\mu} =\mu$. These conditions appear in physical contexts such as the study of a limiting vorticity ...

We study the homogenization of a transmission problem arising in the scattering theory for bounded inhomogeneities with periodic coefficients modeled by the anisotropic Helmholtz equation. The coefficients are assumed to be periodic functions of the fast ...

We obtain classification, solvability, and nonexistence theorems for positive stationary states of reaction-diffusion and Schrödinger systems involving a balance between repulsive and attractive terms. This class of systems contains PDE arising in ...

In large random graphs with fixed edge density and triangle density, it has been observed numerically [C. Radin, K. Ren, and L. Sadun, J. Phys. A, 47 (2014)] that a typical graph is finite-podal, meaning that it has only finitely many distinct “types” of ...

This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant pressure. This is a ...

We study the statistics of Dirichlet eigenvalues of the random Schrödinger operator $-\epsilon^{-2}\Delta^{(\text{\rm d}\mkern0.5mu)}+\xi^{(\epsilon)}(x)$, with $\Delta^{(\text{\rm d}\mkern0.5mu)}$ the discrete Laplacian on ${\Bbb Z}^d$ and $\xi^{(\epsilon)}...

This paper concerns the simultaneous effect of homogenization and of the small noise limit for a second order mean field game (MFG) system with local coupling and quadratic Hamiltonian. We show under some additional assumptions that the solutions of our ...

In this paper, we consider an electrified thin film equation with periodic boundary conditions. When an applied voltage is sufficiently small after a finite time, we prove the global existence of unique solutions around positive constant steady states and ...

In the literature, failure risk analysis on most elasto-perfectly-plastic oscillators is essentially focused on those excited by white noise, which is rather restrictive from the modeling perspective. Our present article is motivated by the study of the ...

A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector field. The analysis ...

This paper studies rates of decay to equilibrium for the Becker--Döring equations with subcritical initial data. In particular, algebraic rates of decay are established when initial perturbations of equilibrium have polynomial moments. This is proved by ...

We study the behavior of certain eigenvalues for magnetic Aharonov--Bohm operators with half-integer circulation and Dirichlet boundary conditions in a planar domain. We analyze the leading term in the Taylor expansion of the eigenvalue function as the pole ...

We discuss a new notion of distance on the space of finite and nonnegative measures on $\Omega \subset {\mathbb R}^d$, which we call the Hellinger--Kantorovich distance. It can be seen as an inf-convolution of the well-known Kantorovich--Wasserstein ...

Let $\Omega\subset\mathbb{R}^3$ be a bounded weak Lipschitz domain with boundary $\Gamma:=\operatorname{\partial}\Omega$ divided into two weak Lipschitz submanifolds $\Gamma_{\tau}$ and $\Gamma_{\nu}$, and let $\varepsilon$ denote an $\mathsf{L}^{\infty}$-...

We offer fairly simple and direct proofs of the asymptotics for the scaled Kramers--Smoluchowski equation in both one and higher dimensions. For the latter, we invoke the sharp asymptotic capacity asymptotics of Bovier et al. [J. Eur. Math. Soc. JEMS, 6 (...

We consider the Dirichlet realization of the operator $-h^2\Delta+iV$ in the semiclassical limit $h\to0$, where $V$ is a smooth real potential with no critical points. For a one-dimensional setting, we obtain the complete asymptotic expansion, in powers of $...

We consider the Ginzburg--Landau energy for a type-I superconductor in the shape of an infinite three-dimensional slab, with two-dimensional periodicity, with an applied magnetic field which is uniform and perpendicular to the slab. We determine the optimal ...

We correct an error in our paper [Convergence of the Allen--Cahn equation with Neumann boundary conditions, SIAM J. Math. Anal., 47 (2015), pp. 1906--1932].

In the author's paper [SIAM J. Math. Anal., 44 (2012), pp. 3786--3805], the author employs the decay estimates of the fundamental solution of the linear dissipative equation to derive the asymptotic expansion for the dissipative equation with the ...