Application of characteristic series for constructing solutions of nonlinear parabolic equations and systems with degeneracy

An extension of the known method of characteristic series (A. F. Sidorov) proposed by the author earlier is used to investigate boundary value problems for a nonlinear differential equation and a nonlinear parabolic system of partial differential equations with degeneracy. New existence theorems for solutions of these problems in the class of analytic functions are proved. In particular, known solutions of the nonlinear heat equation with power dependence of thermal conductivity on temperature are generalized.