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Russian Mathematics

, Volume 55, Issue 2, pp 46–55 | Cite as

One Goursat problem in a Sobolev space

  • I. G. Mamedov
Article

Abstract

In this paper we consider a hyperbolic-type differential equation with L p -coefficients in a three-dimensional space. For this equation we study the Goursat problem with nonclassical boundary constraints not requiringmatched conditions. We prove the equivalence of these boundary conditions to classical ones in the case when one seeks for a solution to the stated problem in an anisotropic space introduced by S. L. Sobolev. In addition, we prove the correct solvability of the Goursat problem by the method of integral equations.

Keywords and phrases

hyperbolic equation three-dimensional Goursat problem equations with Lp-coefficients 

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Copyright information

© Allerton Press, Inc. 2011

Authors and Affiliations

  1. 1.A. I. Guseinov Institute of Cybernetics, National Academy of SciencesRepublic of AzerbaijanBakuRepublic of Azerbaijan

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