This article is cited in 4 papers

On the Boundary-Value Problem for a Class of Equations of Mixed Type in an Unbounded Domai

M. Kh. Ruziev

Institute of Mathematics and Information Technologies of the National Academy of Sciences of Uzbekistan, Tashkent

Abstract: In this paper, we study the boundary-value problem for an equation of mixed type with singular coefficient. The uniqueness of the solution of the problem is proved using the extremum principle and the existence of a solution to the problem is established by the method of integral equations.

Keywords: partial differential equation of mixed type, Gellerstedt problem, boundary-value problem, parabolic degeneracy, extremum principle, Cauchy problem, Darboux formula.

UDC: 517.956.6

Received: 28.12.2009
Revised: 21.05.2011

DOI: 10.4213/mzm8899

 English version: Mathematical Notes, 2012, 92:1, 70–78

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