Self-similar solutions of some model degenerate partial differential equations of the second, third and fourth order
arXiv:2005.11685
Abstract
When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find explicit linearly independent solutions for the system. In this study, we construct self-similar solutions of some model degenerate partial differential equations of the second, third, and fourth order. These self-similar solutions are expressed in terms of hypergeometric functions.
13 pages; to appear in LOBACHEVSKII JOURNAL OF MATHEMATICS