General quasilinear wave equations with localized dissipation in exterior domains

Abstract

We show that the method of commuting vector fields can be applied to quasilinear wave equations with localized dissipations in general exterior domains. This allows us to show long time existence for general quasilinear wave equations with quadratic nonlinearities. Moreover, by assuming that the dissipation is effective in a certain neighborhood of the boundary, we need not place any assumption on the geometry of the domain.