Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate-Reference-Cited by-同舟云学术

Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate

Published:2021-07-01 Issue:0 Volume:0 Page:
ISSN:1569-3945
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Imanuvilov Oleg Y.¹,Kian Yavar²,Yamamoto Masahiro³

Affiliation:

1. Department of Mathematics , Colorado State University , 101 Weber Building , Fort Collins , CO 80523-1874 , USA

2. Centre de Physique Théorique , Aix Marseille Université , CNRS, CPT , Marseille , France

3. Graduate School of Mathematical Sciences , The University of Tokyo , Komaba, Meguro , Tokyo 153-8914 , Japan ; and Honorary Member of Academy of Romanian Scientists, Ilfov, nr. 3, Bucuresti, Romania; Correspondence member of Academia Peloritana dei Pericolanti, Palazzo, Università, Piazza S. Pugliatti 1, 9822 Messina, Italy; and Peoples’ Friendship University of Russia (RUDN University) 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Abstract

Abstract For a parabolic equation in the spatial variable x = ( x 1 , … , x n )

{x=(x_{1},\ldots,x_{n})}

and time t, we consider an inverse problem of determining a coefficient which is independent of one spatial component x n

{x_{n}}

by lateral boundary data. We apply a Carleman estimate to prove a conditional stability estimate for the inverse problem. Also, we prove similar results for the corresponding inverse source problem.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2020-0089/pdf

Reference14 articles.

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