This article is cited in 5 papers

A mixed problem with Tricomi and Frankl conditions for the Gellerstedt equation with a singular coefficient

Gulbakhor M. Mirsaburova

Chair of Differential Equations and Geometry, Termez State University, 43 F. Khodzhaev str., Termez, 190111 Republic of Uzbekistan

Abstract: We consider a generalized Tricomi equation with a singular coefficient. For this equation in a mixed domain we study the corresponding problem, where a part of the boundary characteristic is free of boundary conditions; the deficient Tricomi condition is equivalently substituted by a nonlocal Frankl condition on a segment of the degeneration line. We prove that the stated problem is well-posed.

Keywords: gluing condition, uniqueness of solution, Tricomi singular integral equation, isolated singularity of the first order, Wiener–Hopf equation, index, residue.

UDC: 517.956

Received: 13.04.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:7, 13–26

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