Authors: Menglibay Ruziev; Michael Reissig
Addresses: Institute of Mathematics, National University of Uzbekistan, Tashkent 100125, Uzbekistan ' Institute of Applied Analysis, Technical University Bergakademie Freiberg, 09596 Freiberg, Germany
Abstract: In this paper, we study Tricomi type equations with terms of lower order in the plane. Solutions are required to satisfy conditions on one part of a characteristic in the hyperbolic region of the considered domain and on some parts of the line of parabolic degeneracy. We prove the uniqueness of solutions in suitable spaces of generalised solutions by application of extremum principle. The proof of the existence is based on the theory of singular integral equations, Wiener-Hopf equations and Fredholm integral equations.
Keywords: mixed type equations; index of equation; integral equations; first order isolated singularity; extremum principle; residue; singular coefficients; Tricomi type equations; unbounded domains.
International Journal of Dynamical Systems and Differential Equations, 2016 Vol.6 No.1, pp.1 - 15
Received: 19 Jan 2015
Accepted: 08 Apr 2015
Published online: 05 Feb 2016 *