Special solutions of matrix Gellerstedt equation

Abstract

Fundamental solutions for the Gellerstedt equation and its generalization were obtained in the distribution space using the method applied by I. M. Gelfand and J. Barros-Neto to the studying the Tricomi equation. The degenerating system of the mixed-type partial differential equations was considered, its special solutions were constructed in the regions bounded by the characteristics of these equations (in the hyperbolic halfplane). The elements of the theory of matrices, theory of the generalized functions and the special functions (hypergeometric series) were used for this construction.

Keywords

• fundamental solution
• generalized functions
• matrix functions