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Related papers: On uniqueness of elastic scattering from a cavity

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In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from [Lasiecka, Szulc, and Zochoswki, Nonl. Anal.: Real World Appl., 44, 2018]. An elastic body…

Optimization and Control · Mathematics 2021-09-07 Michael Hintermüller , Axel Kröner

This paper is devoted to existence and uniqueness results for classes of nonlinear diffusion equations (or systems) which may be viewed as regular perturbations of Wasserstein gradient flows. First, in the case. where the drift is a…

Analysis of PDEs · Mathematics 2015-05-07 Guillaume Carlier , Maxime Laborde

We consider the inverse problem of determining the Lam\'{e} parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse…

Analysis of PDEs · Mathematics 2014-12-12 Elena Beretta , Maarten V. de Hoop , Elisa Francini , Sergio Vessella , Jian Zhai

We consider an inverse spectral theory in a domain with the cavity that is bounded by a penetrable inhomogeneous medium. An ODE system is constructed piecewise through the solutions inside and outside the cavity. The ODE system is connected…

Analysis of PDEs · Mathematics 2016-05-18 Lung-Hui Chen

The scattering of wave packets from a single slit and a double slit with the Schr\"odinger equation, is studied numerically and theoretically. The phenomenon of diffraction of wave packets in space and time in the backward region,…

Quantum Physics · Physics 2008-11-26 G. Kälbermann

The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to the problem of cavitation in nonlinear elasticity, in order to re-assess an example of non-uniqueness of entropic weak solutions (with…

Analysis of PDEs · Mathematics 2017-09-05 Jan Giesselmann , Alexey Miroshnikov , Athanasios E. Tzavaras

We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach…

Analysis of PDEs · Mathematics 2025-06-06 Mengjiao Bai , Huaian Diao , Weisheng Zhou

This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine…

Analysis of PDEs · Mathematics 2019-09-04 Peijun Li , Jue Wang , Lei Zhang

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…

Analysis of PDEs · Mathematics 2009-12-16 Xiaodong Liu , Bo Zhang

Scattering poles correspond to non-trivial scattered fields in the absence of incident waves and play a crucial role in the study of wave phenomena. These poles are complex wavenumbers with negative imaginary parts. In this paper, we prove…

Numerical Analysis · Mathematics 2025-07-08 Xiaodong Liu , Jiguang Sun , Lei Zhang

We consider the time-harmonic scalar wave scattering problems with Dirichlet, Neumann, impedance and transmission boundary conditions. Under this setting, we analyze how sensitive diffracted fields and Cauchy data are to small perturbations…

Analysis of PDEs · Mathematics 2020-11-23 Paul Escapil-Inchauspé , Carlos Jerez-Hanckes

In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic Newton equation with an external potential $V$, $V\in C^2$. Using known results,…

Mathematical Physics · Physics 2009-11-11 Alexandre Jollivet

We are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schr\"odinger equation with unknown source and potential terms. The well-posedness of the direct scattering problem is first…

Analysis of PDEs · Mathematics 2020-04-29 Jingzhi Li , Hongyu Liu , Shiqi Ma

We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…

Analysis of PDEs · Mathematics 2018-10-26 Samy Skander Bahoura

This paper is concerned with the inverse acoustic scattering problems by an obstacle or a cavity with a sound-soft or a sound-hard boundary. A direct imaging method relying on the boundary conditions is proposed for reconstructing the shape…

Numerical Analysis · Mathematics 2022-02-21 Deyue Zhang , Yue Wu , Yinglin Wang , Yukun Guo

We consider a prototypical nonlinear parabolic equation whose flux has three distinguished features: it is nonlinear with respect to both the unknown and its gradient, it is homogeneous, and it depends only on the direction of the gradient.…

Analysis of PDEs · Mathematics 2021-09-24 Lorenzo Giacomelli , Salvador Moll , Francesco Petitta

We study uniqueness of Dirichlet problems of second order divergence-form elliptic systems with transversally independent coefficients on the upper half-space in absence of regularity of solutions. To this end, we develop a substitute for…

Analysis of PDEs · Mathematics 2021-08-18 Pascal Auscher , Moritz Egert

We propose a new radiation condition for an infinite inhomogeneous two-dimensional medium which is periodic in the vertical direction and remains invariant in the horizontal direction. The classical Rayleigh-expansion radiation condition…

Analysis of PDEs · Mathematics 2025-11-04 Guanghui Hu , Andreas Rathsfeld , Jiayi Zhang , Ruming Zhang

This paper is concerned with the uniqueness in inverse acoustic and electromagnetic scattering with phaseless near-field data generated by superpositions of two incident plane waves at a fixed frequency. It can be proved that the unknown…

Analysis of PDEs · Mathematics 2023-07-25 Xiaoxu Xu

We reveal how to exploit joint spatial-electromagnetic duality symmetries to obtain invariant scattering properties (including extinction, scattering, absorption) of self-dual scattering systems for incident waves of arbitrary…

Optics · Physics 2020-11-04 Qingdong Yang , Weijin Chen , Yuntian Chen , Wei Liu