Interaction of Singularities of Solution to Semilinear Wave Equation at the Boundary

Abstract

We shall study the reflection of singularities at the boundary for the semilinear wave equation u=F(x,u) in 3 dimensional space-time. We shall show that if a H$F^s$-solution (s>3/2) is conormal in the past to a union of a characteristic plane and its reflected one, then singularities of the solution are reflected as in the linear case, and that if a H$F^s$-solution is conormal to two characteristic planes and their reflected ones in the past, then the solution can be singular not only on the four planes but also on the light cone from the point at which the four planes intersest.