Self-Similar Solutions of a Multidimensional Degenerate Partial Differential Equation of the Third Order

Abstract

When studying the boundary value problems’ solvability for some partial differential equations encountered in applied mathematics, we frequently need to create systems of partial differential equations and explicitly construct linearly independent solutions explicitly for these systems. Hypergeometric functions frequently serve as solutions that satisfy these systems. In this study, we develop self-similar solutions for a third-order multidimensional degenerate partial differential equation. These solutions are represented using a generalized confluent Kampé de Fériet hypergeometric function of the third order.

Keywords

• degenerate partial differential equation
• self-similar solution
• confluent hypergeometric function
• generalized confluent Kampé de Fériet hypergeometric function
• hypergeometric-type system