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We compute quasinormal mode frequencies for static limits of physical black holes - semi-classical black hole solutions to Einstein-Hilbert gravity characterized by the finite formation time of an apparent horizon and its weak regularity.…
This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We…
Analog gravity models of black holes and exotic compact objects provide a unique opportunity to study key properties of such systems in controlled laboratory environments. In contrast to astrophysical systems, analog gravity systems can be…
Some new inequalities of Karamata type are established with a convex function in this paper. The methods of our proof allow us to obtain an extended version of the reverse of Jensen inequality given by Pe{\v} cari\'c and Mi\'ci\'c. Applying…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
The present paper discusses the diffusion approximation of the linear Boltzmann equation in cases where the collision frequency is not uniformly large in the spatial domain. Our results apply for instance to the case of radiative transfer…
Using a simple theoretical model, we demonstrate the emergence of odd-frequency pair amplitudes in conventional Josephson junctions both in the absence of a voltage (DC effect) and in the presence of a finite voltage (AC effect). In both…
We investigate the quantitative unique continuation properties of solutions to second-order elliptic equations with lower-order terms. In particular, we establish quantitative forms of the strong unique continuation property for solutions…
Diffuse domain methods (DDMs) have gained significant attention for solving partial differential equations (PDEs) on complex geometries. These methods approximate the domain by replacing sharp boundaries with a diffuse layer of thickness…
We consider a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. In a previous paper we have found mass-preserving, nonnegative weak solutions of the equation satisfying energy…
We discuss the appearance of odd-frequency spin-triplet s-wave superconductivity, first proposed by Berezinskii [{\it JETP} {\bf 20}, 287 (1974)], on the surface of a topological insulator proximity coupled to a conventional spin-singlet…
This is a continuation of our study [Uhlmann-Zhai, JMPA, 2021] on an inverse boundary value problem for a nonlinear elastic wave equation. We prove that all the linear and nonlinear coefficients can be recovered from the…
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…
Wave equations with energy-dependent potentials appear in many areas of physics, ranging from nuclear physics to black hole perturbation theory. In this work, we use the semi-classical WKB method to first revisit the computation of bound…
We study time-harmonic scattering by a periodic array of penetrable, high-contrast obstacles with small period, confined to a bounded Lipschitz domain. The strong contrast between the obstacles and the background induces subwavelength…
We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some…
We establish a weak-strong uniqueness principle for solutions to entropy-dissipating reaction-diffusion equations: As long as a strong solution to the reaction-diffusion equation exists, any weak solution and even any renormalized solution…
Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…
Von Neumann's original proof of the ergodic theorem is revisited. A uniform convergence rate is established under the assumption that one can control the density of the spectrum of the underlying self-adjoint operator when restricted to…
We consider ASEP on a bounded interval and on a half line with sources and sinks. On the full line, Bertini and Giacomin proved convergence under weakly asymmetric scaling of the height function to the solution of the KPZ equation. We prove…