English
Related papers

Related papers: Stability estimates for the anisotropic wave equat…

200 papers

We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0,2\pi)$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As an inverse data we use a…

Analysis of PDEs · Mathematics 2025-05-27 A. S. Mikhaylov , V. S. Mikhaylov

We consider the inverse problem of identifying an unknown inclusion contained in an elastic body by the Dirichlet-to-Neumann map. The body is made by linearly elastic, homogeneous and isotropic material. The Lam\'e moduli of the inclusion…

Analysis of PDEs · Mathematics 2016-05-31 Giovanni Alessandrini , Michele Di Cristo , Antonino Morassi , Edi Rosset

We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator…

Analysis of PDEs · Mathematics 2025-09-24 A. S. Mikhaylov , V. S. Mikhaylov

We consider a transmission wave equation in two embedded domains in $R^2$, where the speed is $a1 > 0$ in the inner domain and $a2 > 0$ in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that…

Analysis of PDEs · Mathematics 2009-11-13 Lucie Baudouin , Alberto Mercado , Axel Osses

We study a version of Calder\'on's problem for harmonic maps between Riemannian manifolds. By using the higher linearization method, we first show that the Dirichlet-to-Neumann map determines the metric on the domain up to a natural gauge…

Analysis of PDEs · Mathematics 2024-11-05 Sebastián Muñoz-Thon

We study the impedance boundary map (or Robin-to-Robin map) for the Schrodinger equation in open bounded demain at fixed energy in multidimensions. We give global stability estimates for determining potential from these boundary data and,…

Analysis of PDEs · Mathematics 2013-06-27 Mikhail Isaev , Roman Novikov

This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem, and their potential use as target-signatures for fluid-solid…

Analysis of PDEs · Mathematics 2022-01-31 Michael Levitin , Peter Monk , Virginia Selgas

This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…

Mathematical Physics · Physics 2024-01-17 Michael V. Klibanov

We relax the regularity condition on potentials of Schr\"odinger equations in the uniqueness results in \cite{EB} and \cite{IY2} for the inverse boundary value problem of determining a potential by Dirichlet-to-Neumann map.

Mathematical Physics · Physics 2012-08-21 Oleg Yu. Imanuvilov , Masahiro Yamamoto

We consider a strongly damped wave equation on compact manifolds, both with and without boundaries, and formulate the corresponding inverse problems. For closed manifolds, we prove that the metric can be uniquely determined, up to an…

Analysis of PDEs · Mathematics 2023-09-29 Li Li , Yang Zhang

We show that a partial Dirichlet-to-Neumann map, where the measurement set is arbitrarily small, uniquely determines the time-dependent nonlinearity of order three or higher in a semi-linear wave equation up to natural obstructions on a…

Analysis of PDEs · Mathematics 2025-11-13 Boya Liu , Weinan Wang

We consider the inverse problem of determining the time independent scalar potential of the dynamic Schr\"odinger equation in an infinite cylindrical domain, from one Neumann boundary observation of the solution. Assuming that this…

Analysis of PDEs · Mathematics 2015-06-15 Yavar Kian , Quang Sang Phan , Eric Soccorsi

The oscillation of a Laplacian eigenfunction gives a great deal of information about the manifold on which it is defined. This oscillation can be encoded in the nodal deficiency, an important geometric quantity that is notoriously hard to…

Analysis of PDEs · Mathematics 2023-03-07 Gregory Berkolaiko , Yaiza Canzani , Graham Cox , Jeremy L. Marzuola

We study the isotropic elastic wave equation in a bounded domain with boundary with coefficients having jumps at a nested set of interfaces satisfying the natural transmission conditions there. We analyze in detail the microlocal behavior…

Analysis of PDEs · Mathematics 2021-06-02 Plamen Stefanov , Gunther Uhlmann , Andras Vasy

The stability and convergence analysis of high-order numerical approximations for the one- and two-dimensional nonlocal wave equations on unbounded spatial domains are considered. We first use the quadrature-based finite difference schemes…

Numerical Analysis · Mathematics 2022-11-09 Jihong Wang , Jerry Zhijian Yang , Jiwei Zhang

We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic…

Analysis of PDEs · Mathematics 2020-09-23 Anna Kirpichnikova , Jussi Korpela , Matti Lassas , Lauri Oksanen

In this paper, we study the inverse boundary value problem for the wave equation with a view towards an explicit reconstruction procedure. We consider both the anisotropic problem where the unknown is a general Riemannian metric smoothly…

Analysis of PDEs · Mathematics 2017-10-10 Maarten de Hoop , Paul Kepley , Lauri Oksanen

In this paper, we study the rapid stabilization of an unstable wave equation, in which an unknown disturbance is located at the boundary condition. We address two different boundary conditions: Dirichlet- Dirichlet and Dirichlet-Neumann. In…

Optimization and Control · Mathematics 2025-10-07 Patricio Guzmán , Agustín Huerta , Hugo Parada

In this paper we study inverse boundary value problems with partial data for the bi-harmonic operator with first order perturbation. We consider two types of subsets of $\mathbb{R}^{n}(n\geq 3)$, one is an infinite slab, the other is a…

Analysis of PDEs · Mathematics 2013-11-12 Yang Yang

We determine the modulational stability of standing waves with small group velocity in quasi-onedimensional systems slightly above the threshold of a supercritical Hopf bifurcation. The stability limits are given by two different…

patt-sol · Physics 2009-09-25 Hermann Riecke , Lorenz Kramer
‹ Prev 1 4 5 6 7 8 10 Next ›