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When studying boundary value problems for some partial differential equationsarising in applied mathematics, we often have to study the solution of a systemof partial differential equations satisfied by hypergeometric functions andfind explicit linearly independent solutions for the system. In this study, weconstruct self-similar solutions of some model degenerate partial differentialequations of the second, third, and fourth order. These self-similar solutionsare expressed in terms of hypergeometric functions.

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