Self-similar solutions of some model degenerate partial differential equations of the second, third and fourth order

TL;DR

This paper constructs self-similar solutions for certain degenerate partial differential equations of second, third, and fourth order, expressing them explicitly in terms of hypergeometric functions, aiding in boundary value problem analysis.

Contribution

It introduces explicit self-similar solutions for complex degenerate PDEs using hypergeometric functions, expanding analytical tools for these equations.

Findings

Explicit self-similar solutions derived

Solutions expressed in hypergeometric functions

Provides new analytical methods for boundary value problems

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.