On the analytic solvability of a special boundary value problem for the nonlinear heat equation

摘要

In the article we develop an approach to the study of nonlinear problems of mathematical physics, proposed in A. F. Sidorov's school of thought, and apply it to solving boundary value problems with degeneracy for the nonlinear heat (porous medium) equation. The essence of the approach is that the solution of problems is constructed in the form of multiple power series. The convergence of the constructed series is proved by the majorant method. It allows us to propose the existence and uniqueness theorem, which is analogous to the Cauchy-Kovalevskaya theorem for the considered problem. A constructive scheme for finding the coefficients of the series is proposed. A special feature of the study is that the boundary condition is given on a moving closed manifold.