English
Related papers

Related papers: Stability estimate for the Helmholtz equation with…

200 papers

We consider stochastic differential systems driven by a Brownian motion and a Poisson point measure where the intensity measure of jumps depends on the solution. This behavior is natural for several physical models (such as Boltzmann…

Probability · Mathematics 2018-09-25 Vlad Bally , Dan Goreac , Victor Rabiet

This paper is devoted to the exponential stability for one-dimensional linear wave equations with in-domain localized damping and several types of Wentzell (or dynamic) boundary conditions. In a quite general boundary setting, we establish…

Analysis of PDEs · Mathematics 2025-03-31 Abdelhakim Dahmani , Yacine Chitour , Hoai-Minh Nguyen , Christophe Roman

The purpose of this work is to investigate the exponential stability of a second order coupled wave equations by laplacian with one locally internal viscous damping. Firstly, using a unique continuation theorem combined with a Carleman…

Analysis of PDEs · Mathematics 2023-02-20 Mohammad Akil , Mohamed Balegh , Zayd Hajjej

We analyze the stability of stationary solutions of a singular Vlasov type hydrodynamic equation (HE). This equation was derived (under suitable assumptions) as the hydrodynamical scaling limit of the Hamiltonian evolution of a system…

Statistical Mechanics · Physics 2009-11-10 E. Caglioti , N. Chernov , J. L. Lebowitz

The Swift-Hohenberg equation is ubiquitous in the study of bistable dynamics. In this paper, we study the dynamic transitions of the Swift-Hohenberg equation with a third-order dispersion term in one spacial dimension with a periodic…

Dynamical Systems · Mathematics 2020-08-03 Kevin Li

A full viscous quantum hydrodynamic system for particle density, current density, energy density and electrostatic potential coupled with a Poisson equation in one dimensional bounded intervals is studied. First, the existence and…

Analysis of PDEs · Mathematics 2023-07-03 Xiaoying Han , Yuming Qin , Wenlong Sun

In this work, we consider a system of multidimensional wave equations coupled by velocities with one localized fractional boundary damping. First, using a general criteria of Arendt- Batty, by assuming that the boundary control region…

Analysis of PDEs · Mathematics 2021-04-09 Mohammad Akil , Ali Wehbe

In this paper, we address the existence of Fredholm backstepping transformations for self-adjoint and skew-adjoint operators $A$. Under suitable assumptions on the operator $A$ and the possibly unbounded control operator $B$, we prove the…

Optimization and Control · Mathematics 2026-05-19 Ludovick Gagnon , Amaury Hayat , Swann Marx , Shengquan Xiang , Christophe Zhang

Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…

Analysis of PDEs · Mathematics 2016-07-26 Peijun Li , Ganghua Yuan

The linear stability of a stratified shear flow for smooth density profiles is studied. This work focuses on the nature of the stability boundaries of flows in which both Kelvin-Helmholtz and Holmboe instabilities are present. For a fixed…

Fluid Dynamics · Physics 2009-11-11 Alexandros Alexakis

We introduce a numerical method to determine the stability of stationary pulse solutions of the complex Ginzburg-Landau equation. The method involves the computation of the point spectrum of the first-order linear differential operator with…

Spectral Theory · Mathematics 2026-04-01 Erika Gallo , John Zweck , Yuri Latushkin

The goal of this paper is to prove a stable determination of the coefficients for the time-harmonic Maxwell equations, in a Lipschitz domain, by boundary measurements.

Analysis of PDEs · Mathematics 2015-05-18 Pedro Caro

We consider a unique continuation problem for the wave equation given data in a volumetric subset of the space time domain. In the absence of data on the lateral boundary of the space-time cylinder we prove that the solution can be…

Numerical Analysis · Mathematics 2025-10-24 Erik Burman , Lauri Oksanen , Janosch Preuss , Ziyao Zhao

We establish stability inequalities for the problem of determining the potential, appearing in a Sch\"odinger equation, from partial boundary data in the high frequency limit. These stability inequalities hold under the assumption that the…

Analysis of PDEs · Mathematics 2025-01-23 Mourad Choulli

This paper considers the phenomenon of distinct regional frequencies recently observed in some power systems. First, a reduced-order mathematical model describing this behaviour is developed. Then, techniques to solve the model are…

Optimization and Control · Mathematics 2021-04-15 Luis Badesa , Fei Teng , Goran Strbac

This work focuses on the numerical solution of the dynamics of a poroelastic material in the frequency domain. We provide a detailed stability analysis based on the application of the Fredholm alternative in the continuous case, considering…

Numerical Analysis · Mathematics 2024-09-17 Cristian Cárcamo , Alfonso Caiazzo , Felipe Galarce , Joaquín Mura

This paper is focused on the study of an inverse problem for a non-self-adjoint hyperbolic equation. More precisely, we attempt to stably recover a first order coefficient appearing in a wave equation from the knowledge of Neumann boundary…

Analysis of PDEs · Mathematics 2017-10-11 Mourad Bellassoued , Ibtissem Ben Aïcha

This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the obstacle is trapping. There are two resolvent estimates for…

Analysis of PDEs · Mathematics 2019-12-04 Simon N. Chandler-Wilde , Euan A. Spence , Andrew Gibbs , Valery P. Smyshlyaev

This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…

Analysis of PDEs · Mathematics 2018-08-17 Gang Bao , Peijun Li , Yue Zhao

We consider a space-homogeneous gas of {\it inelastic hard spheres}, with a {\it diffusive term} representing a random background forcing (in the framework of so-called {\em constant normal restitution coefficients} $\alpha \in [0,1]$ for…

Analysis of PDEs · Mathematics 2010-02-02 Stéphane Mischler , Clément Mouhot