Electron. J. Diff. Equ., Vol. 2014 (2014), No. 193, pp. 1-9.

Properties of solutions to Neumann-Tricomi problems for Lavrent'ev-Bitsadze equations at corner points

Makhmud A. Sadybekov, Nurgissa A. Yessirkegenov

Abstract:
We consider the Neumann-Tricomi problem for the Lavrent'ev-Bitsadze equation for the case in which the elliptic part of the boundary is part of a circle. For the homogeneous equation, we introduce a new class of solutions that are not continuous at the corner points of the domain and construct nontrivial solutions in this class in closed form. For the nonhomogeneous equation, we introduce the notion of an n-regular solution and prove a criterion for the existence of such a solution.

Submitted July 9, 2014. Published September 16, 2014.
Math Subject Classifications: 35M10.
Key Words: Neumann-Tricomi problem; n-regular solution; Lavrent'ev-Bitsadze equation.

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Makhmud A. Sadybekov
Institute of Mathematics and Mathematical Modeling
125 Pushkin str., 050010 Almaty, Kazakhstan
email: makhmud-s@mail.ru
Nurgissa A. Yessirkegenov
Institute of Mathematics and Mathematical Modeling
125 Pushkin str., 050010 Almaty, Kazakhstan
email: nurgisa@hotmail.com

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