Inverse free boundary problem for degenerate parabolic equation

Abstract

The coefficient inverse problem for a degenerate parabolic equation is studied in a free boundary domain. The degeneration of the equation is caused by time dependent function at the higher order derivative of unknown function. It is assumed that the coefficient at the minor derivative of the equation is a polynomial of the first order for the space variable with two unknown time depended functions. The conditions of existence and uniqueness of the classical solution to such inverse problem are established for the weak degeneration case at the Dirichlet boundary conditions and the values of heat moments as overdetermination conditions.