Stability estimate for a partial data inverse problem for the convection-diffusion equation

Soumen Senapati; Manmohan Vashisth

doi:10.3934/eect.2021060

Article Contents

2022, Volume 11, Issue 5: 1681-1699. Doi: 10.3934/eect.2021060

This issue Previous Article Controlled singular evolution equations and Pontryagin type maximum principle with applications Next Article Convergence of random attractors towards deterministic singleton attractor for 2D and 3D convective Brinkman-Forchheimer equations

Stability estimate for a partial data inverse problem for the convection-diffusion equation

Soumen Senapati^1, and
Manmohan Vashisth^2, ,

1.
TIFR Centre for Applicable Mathematics, Bangalore 560065, India
2.
Department of Mathematics, Indian Institute of Technology, Jammu 181221, India

^*Corresponding author: Manmohan Vashisth
^*Corresponding author: Manmohan Vashisth

Received: March 31, 2021

Revised: August 31, 2021

Early access: December 2021

Published: October 2022

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Abstract

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 $ n\ge 2 $, we show the convection term (modulo the gauge term) admits log-log stability, whereas log-log-log stability estimate is obtained for the density coefficient.

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Mathematics Subject Classification: 35R30, 35K20.

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