SOLUTION OF ONE CONJUGATION PROBLEM FOR A DEGENERATE HEAT EQUATION

Abstract

Problems of thermal conductivity with discontinuous coefficients and degenerate equations of parabolic type, each separately, have long been well studied. Initial-boundary value problems for the degenerate heat equation with discontinuous coefficients are practically not studied.

     This paper is devoted to the study of a conjugation problem for a degenerate heat equation with discontinuous coefficients. First, the solution of two auxiliary problems is constructed using the Fourier transform and Laplace transform, then the solution of the conjugation problem for the degenerate heat equation is found using the solutions of auxiliary problems.  A fundamental solution of the problem is constructed and an estimate of its derivatives is found. The obtained result is used in the study of initial-boundary value problems for the degenerate heat equation with discontinuous coefficients in the Sobolev and Helder classes