Hypergeometric Expansions of Solutions of the Degenerating Model Parabolic Equations of the Third Order

In investigation of boundary-value problems for certain partial differential equations arising in applied mathematics, we often need 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 investigation, we construct special solutions for a certain class of degenerating differential equations of parabolic type of a high order. These special solutions are expressed in terms of hypergeometric functions of one variable.