Asymptotics of the Green function and Poisson kernels of a mixed parabolic problem in a cone. I.

Abstract

General boundary value problems for $2b$-parabolic equations in a multidimensional cone are considered. Theorems on solvability and smoothness of solutions are proved. Infinite asymptotic expansions of solutions are obtained in a neighbourhood of the conic vertex. The representations for the coefficients of these expansions are also obtained. At last formal asymptotics of the Green function and the Poisson kernels are obtained.