The existence and singularity structures of low regularity solutions to higher order degenerate hyperbolic equations

Abstract

This paper is a continuation of our partial work in [21], where we established that the bounded local solution u(t, x) exists and is piecewise smooth for the second order degenerate hyperbolic equation (partial derivative(2)(t) - t(m)Delta(x))u = f (t, x, u) with the initial data of C-1-piecewise smooth u(0, x) and piecewise smooth partial derivative(t)u(0, x). In the present paper, we will consider the lower regularity solution of the higher order degenerate hyperbolic equation in the category of discontinuous and even unbounded functions. (C) 2013 Elsevier Inc. All rights reserved.