Inverse problem for a two-dimensional strongly degenerate heat equation

Abstract

This article concerns the existence and uniqueness of solutions in the problem of identifying the leading coefficient in a two-dimensional heat equation. We suppose that unknown coefficient depends on the time variable and the equation is strongly degenerate. Applying Schauder fixed-point theorem, we find conditions for existence of a classical solution.

Keywords

• Inverse problem
• strongly degenerate heat equation
• Green function
• classical solution