Фундаментальні розв’язки задачі Коші для одного класу вироджених параболічних рівнянь та їх застосування

Abstract

The degenerate parabolic equations are considered that are the same as the Kolmogorov's equation of diffusion with inertia and degenerations on the initial hyperplane. Fundamental solutions of the Cauchy problem for such equations are constructed, their properties are investigated, and some applications of these properties are obtained. Separately, necessary and sufficient conditions are found under which the solutions of the homogeneous equations with a weak degeneration on the initial hyperplane are represented in the form of Poisson's integrals of the functions or generalized Borel measures from special spaces.