This article is cited in 3 papers

A problem with the Frankl and Bitsadze–Samarskii condition on the line of degeneracy and on parallel characteristics for a mixed-type equation

M. Kh. Ruziev

Department of Differential Equations, Institute of Mathematics and Information Technologies, National Academy of Sciences of Republic of Uzbekistan, Tashkent, Republic of Uzbekistan

Abstract: In this paper we study a boundary-value problem with the Frankl and Bitsadze–Samarskii condition on the line of degeneracy and on parallel characteristics for a mixed-type equation with a singular coefficient. We prove the existence of a solution by the method of integral equations, and we do its uniqueness with the help of the extremum principle.

Keywords: extremum principle, unique solvability, existence of solution, integral equations.

UDC: 517.956

Received: 31.03.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:8, 35–43

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