Lipschitz stability in determination of coefficients in a two-dimensional Boussinesq system by arbitrary boundary observation

Mourad Bellassoued; Chaima Moufid

doi:10.3934/dcdss.2020394

Article Contents

2021, Volume 14, Issue 8: 2671-2692. Doi: 10.3934/dcdss.2020394

This issue Previous Article Global attractor for a one dimensional weakly damped half-wave equation Next Article Damping, stabilization, and numerical filtering for the modeling and the simulation of time dependent PDEs

Lipschitz stability in determination of coefficients in a two-dimensional Boussinesq system by arbitrary boundary observation

Mourad Bellassoued^, and
Chaima Moufid

University of Tunis El Manar, National Engineering School of Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis, Tunisia

^* Corresponding author: Mourad Bellassoued
^* Corresponding author: Mourad Bellassoued

Received: October 31, 2019

Revised: March 31, 2020

Early access: June 2020

Published: August 2021

The authors are supported by the Tunisian Research Program PHC-UTIQUE 19G-1507

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Abstract

In this paper, we consider the inverse problem of determining two spatially varying coefficients appearing in the two-dimensional Boussinesq system from observed data of velocity vector and the temperature in a given arbitrarily subboundary. Based on Carleman estimates, we prove a Lipschitz stability result.

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Mathematics Subject Classification: Primary: 35R30, 35M33; Secondary: 76M21.

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