Solution of Cauchy Problem for the Generalized Gellerstedt Equation
Abdumauvlen BerdyshevInstitute of Mathematics, Physics and Computer Science, Abay University and Institute of Information and Computational Technologies, Almaty, KazakhstanAnvar HasanovInstitute of Mathematics, Uzbekistan Academy of Sciences, 100170, Tashkent, UzbekistanZh. A. AbdiramanovInstitute of Mathematics, Physics and Computer Science, Abay University and Institute of Information and Computational Technologies, Almaty, Kazakhstan
ABI
Abstract
In this paper, the unique solvability of the Cauchy problem for a generalized hyperbolic Gellersted equation with two lines of degeneracy of different order is studied. A modified initial problem is formulated. By using the Riemann method the solution of this problem is constructed in an explicit form inside characteristic triangle. The constructed Riemann function is expressed by special Appell functions and Gauss hypergeometric functions of two variables.