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.

中文翻译：

---

一些模型的二阶，三阶和四阶退化偏微分方程的自相似解

摘要

在研究应用数学中出现的某些偏微分方程的边值问题时，我们经常必须研究由超几何函数满足的偏微分方程系统的解，并找到该系统的显式线性独立解。在这项研究中，我们构造了二阶，三阶和四阶模型退化的偏微分方程的自相似解。这些自相似解用超几何函数表示。