Interaction of two nonlinear waves at the boundary (Q1110733)

The author shows that anomalous singularities of nonlinear wave equations may occur when two characteristic surfaces carrying singularities hit a boundary point at the same time. He deals with the Dirichlet boundary value problem of the following nonlinear equations \[ \partial^ 2u/\partial t^ 2-\partial^ 2/\partial x^ 2-\partial^ 2u/\partial y^ 2=f(\partial u/\partial y),\quad u=0\quad on\quad \{y=0\} \] under certain conditions on the nonlinear term f, and constructs a solution u such that; for \(t<0\) the solution has singularity on two characteristic surfaces, and for \(t>0\) it has another singularity on the half of forward light cone with vertex at the origin besides those characteristic surfaces.