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In this paper we consider an interior stabilization problem for the wave equation with dynamic boundary delay.We prove some stability results under the choice of damping operator. The proof of the main result is based on a frequency domain…

Analysis of PDEs · Mathematics 2016-02-10 Kaïs Ammari , Stéphane Gerbi

In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, we show that the ill-posedness decreases when we…

Analysis of PDEs · Mathematics 2011-10-25 Sei Nagayasu , Gunther Uhlmann , Jenn-Nan Wang

In this paper, the simultaneous identification of damping or anti-damping coefficient and initial value for some PDEs is considered. An identification algorithm is proposed based on the fact that the output of system happens to be…

Analysis of PDEs · Mathematics 2016-05-18 Zhi-Xue Zhao , Mapundi Kondwani Banda , Bao-Zhu Guo

In this work we establish log-type stability estimates for the inverse potential and conductivity problems with partial Dirichlet-to-Neumann map, where the Dirichlet data is homogeneous on the inaccessible part. This result, to some extent,…

Analysis of PDEs · Mathematics 2007-08-27 Horst Heck , Jenn-Nan Wang

We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined…

Analysis of PDEs · Mathematics 2024-09-10 Giovanni Covi , Jesse Railo , Teemu Tyni , Philipp Zimmermann

Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…

Analysis of PDEs · Mathematics 2014-09-29 Lucie Baudouin , Sylvain Ervedoza , Axel Osses

We are concerned with the problem of determining the damping boundary coefficient appearing in a dissipative wave equation from a single boundary measurement. We prove that the uniqueness holds at the origin provided that the initial…

Analysis of PDEs · Mathematics 2015-03-17 Mourad Choulli , Kaïs Ammari

In this article, stability estimates are given for the determination of the zeroth-order bounded perturbations of the biharmonic operator when the boundary Neumann measurements are made on the whole boundary and on slightly more than half…

Analysis of PDEs · Mathematics 2015-06-03 Anupam Pal Choudhury , Venkateswaran P. Krishnan

This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…

Analysis of PDEs · Mathematics 2021-03-02 Peijun Li , Xiaohua Yao , Yue Zhao

We establish a logarithmic stability inequality for the inverse problem of determining the non linear term, appearing in a semilinear BVP, from the corresponding Dirichlet-to-Neumann map (abbreviated to DtN map in the rest of this text).…

Analysis of PDEs · Mathematics 2020-09-08 Mourad Choulli , Guanghui Hu , Masahiro Yamamoto

This paper investigates inverse potential problems of wave equations with cubic nonlinearity. We develop a methodology for establishing stability estimates for inversion of lower order coefficients. The new ingredients of our approach…

Analysis of PDEs · Mathematics 2025-01-22 Xi Chen , Shuai Lu , Ruochong Zhang

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

This paper investigates stability estimates for inverse source problems in the stochastic polyharmonic wave equation, where the source is represented by white noise. The study examines the well-posedness of the direct problem and derives…

Analysis of PDEs · Mathematics 2024-10-15 Peijun Li , Zhenqian Li , Ying Liang

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…

Numerical Analysis · Mathematics 2014-06-11 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu , Otmar Scherzer

We give effectivized Holder-logarithmic energy and regularity dependent stability estimates for the Gel'fand inverse boundary value problem in dimension $d=3$. This effectivization includes explicit dependance of the estimates on…

Analysis of PDEs · Mathematics 2015-06-19 Mikhail Isaev , Roman Novikov

In this paper, we present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary…

Analysis of PDEs · Mathematics 2026-02-06 S. E. Chorfi , G. El Guermai , L. Maniar , W. Zouhair

In this paper we consider a boundary stabilization problem for the wave equation with interior delay. We prove an exponential stability result under some Lions geometric condition. The proof of the main result is based on an identity with…

Analysis of PDEs · Mathematics 2010-05-17 K. Ammari , S. Nicaise , C. Pignotti

In this work we study the phenomenon of increasing stability in the inverse boundary value problem for the Schr\"odinger equation. This problem was previously considered by Isakov in which he discussed the phenomenon in different ranges of…

Analysis of PDEs · Mathematics 2013-02-06 V Isakov , S Nagayasu , G Uhlmann , J-N Wang

We consider the inverse problem of determining the isotropic inhomogeneous electromagnetic coefficients of the non-stationary Maxwell equations in a bounded domain of R^3, from a finite number of boundary measurements. Our main result is a…

Analysis of PDEs · Mathematics 2015-06-11 Mourad Bellassoued , Michel Cristofol , Eric Soccorsi

In this article, we study the stability in the inverse problem of determining the time-dependent convection term and density coefficient appearing in the convection-diffusion equation, from partial boundary measurements. For dimension…

Analysis of PDEs · Mathematics 2022-04-19 Soumen Senapati , Manmohan Vashisth