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We consider the recovery of a potential associated with a semi-linear wave equation on $\mathbb{R}^{n+1}$, $n\geq 1$. We show a H\"older stability estimate for the recovery of an unknown potential $a$ of the wave equation $\square u +a…

Analysis of PDEs · Mathematics 2020-06-24 Matti Lassas , Tony Liimatainen , Leyter Potenciano-Machado , Teemu Tyni

We formulate an inverse problem for an uncoupled space-time fractional Schr\"odinger equation on closed manifolds. Our main goal is to determine the fractional powers and the Riemannian metric (up to an isometry) simultaneously from the…

Analysis of PDEs · Mathematics 2024-10-29 Li Li

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 uniqueness in an inverse Schr\"odinger problem in a bounded domain in $\mathbb{R}^2$ given the Dirichlet-to-Neumann map on part of the boundary. On the remaining boundary we impose a new type of singular boundary condition with…

Analysis of PDEs · Mathematics 2018-09-19 Freddy J. F. Symons

A numerical method for the Dirichlet initial boundary value problem for the elastic equation in the exterior and unbounded region of a smooth closed simply connected 2-dimensional domain, is proposed and investigated. This method is based…

Numerical Analysis · Mathematics 2024-02-23 Roman Chapko , Leonidas Mindrinos

In this article we focus on inverse problems for a semilinear elliptic equation. We show that a potential $q$ in $L^{n/2+\varepsilon}$, $\varepsilon>0$, can be determined from the full and partial Dirichlet-to-Neumann map. This extends the…

Analysis of PDEs · Mathematics 2023-01-13 Janne Nurminen

We discuss an initial-boundary value problem for a fractional diffusion equation with Caputo time-fractional derivative where the coefficients are dependent on spatial and time variables and the zero Dirichlet boundary condition is…

Analysis of PDEs · Mathematics 2018-06-12 Adam Kubica , Masahiro Yamamoto

Consider a three dimensional piecewise homogeneous anisotropic elastic medium $\Omega$ which is a bounded domain consisting of a finite number of bounded subdomains $D_\alpha$, with each $D_\alpha$ a homogeneous elastic medium. One typical…

Analysis of PDEs · Mathematics 2017-04-13 Cătălin I. Cârstea , Naofumi Honda , Gen Nakamura

We study a class of fractional parabolic equations involving a time-dependent magnetic potential and formulate the corresponding inverse problem. We determine both the magnetic potential and the electric potential from the exterior partial…

Analysis of PDEs · Mathematics 2021-01-21 Li Li

We study the well-posedness of a semilinear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map.…

Analysis of PDEs · Mathematics 2022-03-30 Li Li

This licentiate thesis is concerned with an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, for compactly supported potentials $A\in W^{1,\infty}(\bar{\mathbb{R}^3_{-}},\R^3)$ and $q \in…

Analysis of PDEs · Mathematics 2012-09-06 Valter Pohjola

We consider the inverse problem of recovering the magnetic and potential term of a magnetic Schr\"{o}dinger operator on certain compact Riemannian manifolds with boundary from partial Dirichlet and Neumann data on suitable subsets of the…

Analysis of PDEs · Mathematics 2018-10-10 Sombuddha Bhattacharyya

In this paper, a strongly damped semilinear wave equation with a general nonlinearity is considered. With the help of a newly constructed auxiliary functional and the concavity argument, a general finite time blow-up criterion is…

Analysis of PDEs · Mathematics 2020-10-22 Hui Yang , Yuzhu Han

In this paper we prove uniqueness for some parameter identification problems for the JMGT equation, a third order in time quasilinear PDE in nonlinear acoustics. The coefficients to be recovered are the space dependent nonlinearity…

Analysis of PDEs · Mathematics 2023-05-09 Barbara Kaltenbacher

In this paper, we study the inverse problem of finding a time-dependent multiplier of the right-hand side of a time-fractional one-dimensional diffusion equation with variables coefficients in the case where the usual Cauchy, homogeneous…

Analysis of PDEs · Mathematics 2024-11-15 D. K. Durdiev

This article considers a unilateral contact problem for the wave equation. The problem is reduced to a variational inequality for the Dirichlet-to-Neumann operator for the wave equation on the boundary, which is solved in a saddle point…

Numerical Analysis · Mathematics 2018-02-06 Heiko Gimperlein , Fabian Meyer , Ceyhun Oezdemir , Ernst P. Stephan

We consider the Dirichlet boundary value problem for graphical maximal submanifolds inside Lorentzian type ambient spaces, and obtain general existence and uniqueness results which apply to any codimension.

Differential Geometry · Mathematics 2018-08-01 Yang Li

We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and right hand side on smooth…

Analysis of PDEs · Mathematics 2014-04-07 Guenther Hoermann , Michael Kunzinger , Roland Steinbauer

In this paper, we study inverse boundary problems associated with semilinear parabolic systems in several scenarios where both the nonlinearities and the initial data can be unknown. We establish several simultaneous recovery results…

Analysis of PDEs · Mathematics 2022-10-12 Yi-Hsuan Lin , Hongyu Liu , Xu Liu , Shen Zhang

This paper considers the inverse boundary value problem for the equation $\nabla\cdot(\sigma\nabla u+a|\nabla u|^{p-2}\nabla u)=0$. We give a procedure for the recovery of the coefficients $\sigma$ and $a$ from the corresponding…

Analysis of PDEs · Mathematics 2021-02-03 Cătălin I. Cârstea , Manas Kar