Title: The Gellerstedt problem for a parabolic-hyperbolic equation of the second kind

Authors: N.K. Mamadaliev

Addresses: National University of Uzbekistan, Tashkent

Abstract: We investigate the well-posedness theory for the Gellerstedt problem, which consists of a singular second-order partial differential equation of mixed parabolic-hyperbolic type. Our proof relies on a new representation formula which reduces the problem to a Volterra integral equation of the second kind.

Keywords: boundary value problems; Gellerstedt problem; differential equations; hyperbolic; second kind; generalised solution; class R; modified Cauchy problem; parabolic-hyperbolic type; Volterra integral equation; hypergeometric identity.

DOI: 10.1504/IJDSDE.2007.016512

International Journal of Dynamical Systems and Differential Equations, 2007 Vol.1 No.2, pp.102 - 108

Published online: 06 Jan 2008 *

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