Lipschitz stability for an inverse source problem in anisotropic parabolic equations with dynamic boundary conditions

El Mustapha Ait Ben Hassi; Salah-Eddine Chorfi; Lahcen Maniar; Omar Oukdach

doi:10.3934/eect.2020094

Article Contents

2021, Volume 10, Issue 4: 837-859. Doi: 10.3934/eect.2020094

This issue Previous Article Hadamard well-posedness for a structure acoustic model with a supercritical source and damping terms Next Article Stabilization of higher order Schrödinger equations on a finite interval: Part I

Lipschitz stability for an inverse source problem in anisotropic parabolic equations with dynamic boundary conditions

Cadi Ayyad University, Faculty of Sciences Semlalia, LMDP, UMMISCO (IRD-UPMC) B.P. 2390, Marrakesh, Morocco

^* Corresponding author: Lahcen Maniar
^* Corresponding author: Lahcen Maniar

Received: January 31, 2020

Revised: May 31, 2020

Early access: September 2020

Published: December 2021

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Abstract

In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous recovery of two source terms from a single measurement and interior observations, based on a recent Carleman estimate for such problems.

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Mathematics Subject Classification: Primary:35R30;Secondary:35K05.

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