SIMULTANEOUS IDENTIFICATION OF THE RIGHT-HAND SIDE AND TIME-DEPENDENT COEFFICIENTS IN A TWO-DIMENSIONAL PARABOLIC EQUATION-Reference-Cited by-同舟云学术

SIMULTANEOUS IDENTIFICATION OF THE RIGHT-HAND SIDE AND TIME-DEPENDENT COEFFICIENTS IN A TWO-DIMENSIONAL PARABOLIC EQUATION

Published:2024-02-23 Issue:1 Volume:29 Page:90-108
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
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Author:

Mehraliyev Yashar T.¹,Huntul Mousa J.²,Azizbayov Elvin I.³

Affiliation:

1. Department of Differential and Integral Equations, Baku State University, Z. Khalilov Str. 23, AZ1148 Baku, Azerbaijan

2. Department of Mathematics, Faculty of Science, Jazan University, Al Maarefah Rd, P.O. Box 114, Jazan, Saudi Arabia

3. Department of Control for Intelligent Systems, Academy of Public Administration under the President of the Republic of Azerbaijan, Lermontov Str. 74, AZ1001 Baku, Azerbaijan; Department of Mathematics, Khazar University, Baku, Azerbaijan

Abstract

This paper investigates the simultaneous identification of time-dependent lowest and source terms in a two-dimensional (2D) parabolic equation from the additional measurements. To investigate the solvability of the inverse problem, we first examine an auxiliary inverse boundary value problem and prove its equivalence to the original problem in a certain sense. Then, applying the contraction mappings principle existence and uniqueness of the solution of an equivalent problem is proved. Furthermore, using the equivalency, the existence and uniqueness theorem for the classical solution of the original problem is obtained and some discussions on the numerical solutions for this inverse problem are presented including numerical examples.

Publisher

Vilnius Gediminas Technical University

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