REFLECTION OF DISCONTINUITIES FOR NONLINEAR WEAKLY STABLE BOUNDARY VALUE PROBLEMS

Abstract

This paper is concerned with the reflection of nonlinear discontinuous waves, for weakly well-posed hyperbolic boundary value problems, satisfying the (WR) condition, that is in a case where the IBVP is neither strongly stable, nor strongly unstable. We study how the singularities of a striated solution are reflected when the solution hits the boundary. We prove striated estimates and L∞ estimates and observe the loss of one derivative: we show that a discontinuity of the gradient of the solution across a hyperplane can be reflected in a discontinuity across a hyperplane of the solution itself.