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Open Access Research

A problem with conditions given on inner characteristics and on the line of degeneracy for a mixed-type equation with singular coefficients

Menglibay Kholtojibaevich Ruziev

Author Affiliations

Institute of Mathematics, National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan

Boundary Value Problems 2013, 2013:210  doi:10.1186/1687-2770-2013-210

Published: 12 September 2013

Abstract

In an unbounded domain, we consider a problem with conditions given on inner characteristics in a hyperbolic part of the considered domain and on some parts of the line of parabolic degeneracy. We prove the unique solvability of the mentioned problem with the help of the extremum principle. The proof of solvability is based on the theory of singular integral equations, Wiener-Hopf equations and Fredholm integral equations.