Reflection of discontinuities for nonlinear weakly stable boundary value problems (Q2905741)

This article 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. The author investigates how the singularities of a striated solution are reflected when the solution hits the boundary. The article proves striated estimates and \(L^\infty \) estimates and derives the loss of one derivative: the author demonstrates 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.