Simultaneous identification of the right-hand side and time-dependent coefficients in a two-dimensional parabolic equation

• Published in: Mathematical modelling and analysis Vol. 29; no. 1; pp. 90 - 108
• Main Authors: Mehraliyev, Yashar T., Huntul, Mousa J., Azizbayov, Elvin I.
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 23.02.2024
• Subjects: 2D parabolic equation; Boundary conditions; Boundary value problems; classical solution; Equivalence; Existence theorems; Fourier method; Functions, Inverse; Identification; Integral equations; inverse identification problem; Inverse problems; nonlinear optimization; Partial differential equations; Tests, problems and exercises; Tikhonov regularization; Time dependence; Uniqueness theorems; Azerbaijan; Tikhonov regularization; inverse identification problem; 2D parabolic equation; classical solution; Fourier method; nonlinear optimization
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2024.17974

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.