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We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…

Analysis of PDEs · Mathematics 2016-09-21 Kais Ammari , Mourad Choulli , Faouzi Triki

This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…

Analysis of PDEs · Mathematics 2018-12-03 Jianliang Li , Tapio Helin , Peijun Li

We prove a stability result in the hybrid inverse problem of recovering the electrical conductivity from partial knowledge of one current density field generated inside a body by an imposed boundary voltage. The region where interior data…

Mathematical Physics · Physics 2016-02-17 Carlos Montalto , Alexandru Tamasan

In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the…

Numerical Analysis · Mathematics 2026-01-23 Shutong Hou , Mourad Sini , Haibing Wang

This paper investigates the identification of two coefficients in a coupled hyperbolic system with an observation on one component of the solution. Based on the the Carleman estimate for coupled wave equations a logarithmic type stability…

Analysis of PDEs · Mathematics 2020-11-19 Fangfang Dou , Masahiro Yamamoto

Inverse nodal problem on diffusion operator is the problem of finding the potential functions and parameters in the boundary conditions by using nodal data. In particular, we solve the reconstruction and stability problems using nodal set…

Spectral Theory · Mathematics 2013-02-19 Emrah Yilmaz , Hikmet Kemaloglu

We are concerned with an inverse problem associated with the fractional Helmholtz system that arises from the study of viscoacoustics in geophysics and thermoviscous modelling of lossy media. We are particularly interested in the case that…

Analysis of PDEs · Mathematics 2018-03-28 Xinlin Cao , Hongyu Liu

A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…

Mathematical Physics · Physics 2007-05-23 S. Gutman , A. G. Ramm , W. Scheid

In this paper, we study the performance of Full Waveform Inversion (FWI) from time-harmonic Cauchy data via conditional well-posedness driven iterative regularization. The Cauchy data can be obtained with dual sensors measuring the pressure…

Analysis of PDEs · Mathematics 2019-06-05 Giovanni Alessandrini , Maarten V. de Hoop , Florian Faucher , Romina Gaburro , Eva Sincich

In this paper, we study the partial data inverse boundary value problem for the Schrodinger operator at a high frequency k>=1 in a bounded domain with smooth boundary in Rn, n>=3. Assuming that the potential is known in a neighborhood of…

Analysis of PDEs · Mathematics 2023-04-25 Xiaomeng Zhao , Ganghua Yuan

We consider the density field $f(x)$ generated by a volume source $\mu(y)$ in $D$ which is a domain in $\R^3$. For two disjoint segments $\gamma, \Gamma_1$ on a straight line in $\R^3 \setminus \ooo{D}$, we establish a conditional stability…

Analysis of PDEs · Mathematics 2019-04-29 Y. Chen , J. Cheng , G. Floridia , Y. Wada , M. Yamamoto

We consider Helmholtz problems with a perturbed wave speed, where the single-signed perturbation is linear in a parameter $z$. Both the wave speed and the perturbation are allowed to be discontinuous (modelling a penetrable obstacle). We…

Analysis of PDEs · Mathematics 2024-07-26 Euan A. Spence , Jared Wunsch , Yuzhou Zou

This paper offers an extensive exploration of nonradiating sources for the two- and three-dimensional biharmonic wave equations. Various equivalent characterizations are derived to reveal the nature of a nonradiating source. Additionally,…

Analysis of PDEs · Mathematics 2023-09-06 Peijun Li , Jue Wang

In this article, we discuss quantitative Runge approximation properties for the acoustic Helmholtz equation and prove stability improvement results in the high frequency limit for an associated partial data inverse problem modelled on…

Analysis of PDEs · Mathematics 2021-01-12 María Ángeles García-Ferrero , Angkana Rüland , Wiktoria Zatoń

In this article, we investigate both forward and backward problems for coupled systems of time-fractional diffusion equations, encompassing scenarios of strong coupling. For the forward problem, we establish the well-posedness of the…

Analysis of PDEs · Mathematics 2025-08-19 Dian Feng , Yikan Liu , Shuai Lu

This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…

Numerical Analysis · Mathematics 2025-10-24 Kai Yu , Zhiyuan Li , Yikan Liu

This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…

Numerical Analysis · Mathematics 2025-01-31 Zhiyuan Li , Chunlong Sun , Xiangcheng Zheng

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

The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier-Stokes equations. We develop a separation of variables representation for this equation in polar…

Numerical Analysis · Mathematics 2017-10-17 Travis Askham

We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…

Analysis of PDEs · Mathematics 2015-05-11 Sascha Trostorff