Inverse Problem for the Parabolic Equation With General Weak Degeneration

Abstract

In the rectangle with known boundary we consider a coefficient inverse problem for the degenerate parabolic equation with given initial condition, Dirichlet boundary conditions and the values of the heat moments as the overdetermination conditions. The minor coefficient of the equation is a polynomial of the first power with respect to the space variable with two unknown time-dependent coefficients. The degeneration of the equation is caused by the power function at the time derivative. Applying the Schauder fixed-point theorem we establish conditions of existence of the classical local in time solution to this problem. The global uniqueness is based on the properties of the solutions of the integral Voltera equations of second kind with integrable kernels. The case of weak degeneration is investigated.