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

This paper is a continuation of our partial work in [21], where we established that the bounded local solution u(t,x)u(t,x) exists and is piecewise smooth for the second order degenerate hyperbolic equation (∂t2−tmΔx)u=f(t,x,u) with the initial data of C1C1-piecewise smooth u(0,x)u(0,x) and piecewise smooth ∂tu(0,x)∂tu(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.