Interaction of Conormal Waves with Different Singularities for Semi-linear Equations

Abstract

We consider a solution of the semi-linear partial differential equations in higher space dimensions. We show that if there exist two characteristic hypersurface bearing different weak singularities intersect transversally, and another one characteristic hypersurface issues from above intersection, then the solution would be conormal with respect to the union of these surfaces, and satisfy the so-called “sum law”.