Two-dimensional inverse quasilinear parabolic problem with periodic boundary condition

ABSTRACT

In this study, we consider a coefficient problem of a quasi-linear two-dimensional parabolic inverse problem with periodic boundary and integral over determination conditions. We prove the existence, uniqueness and continuously dependence upon the data of the solution by iteration method. Also, we consider numerical solution for this inverse problem by using linearization and the implicit finite-difference scheme.

KEYWORDS:

• Finite-difference method
• inverse problem
• parabolic equation
• periodic boundary conditions

AMS SUBJECT CLASSIFICATIONS:

• 35K55
• 35K70

Acknowledgements

The authors are grateful to the reviewers for many valuable suggestions and constructive comments that have greatly improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.