ON THE SOLUTION OF THE CAUCHY PROBLEM FOR A DEGENERATING HYPERBOLIC EQUATION OF THE SECOND KIND

Abstract

In the scientific literature, degenerate hyperbolic equations are usually divided into two types: equations of the first and second kind. For equations of the first kind, the line of parabolic degeneracy is the locus of cusp points of families of characteristics, and for equations of the second kind, the line of parabolic degeneracy is a special characteristic - the envelope of a family of characteristics, which complicates the study of equations of the second kind, so degenerate hyperbolic equations of the second kind are relatively little studied in all respects than equations of the first kind. In this paper, we prove that the solution of the Cauchy problem for a single equation of the second kind, found by the Riemann method, is indeed a twice continuously differentiable solution of the problem in a closed domain.