Time asymptotics for the biharmonic wave equation in exterior domains

Abstract

We consider initial-boundary value problems for the plate equation u″(t,x)+Δ²u(t,x)=f(x) in exterior domains of odd dimension. Especially the boundary condition Δu=∂Δu/∂n=0 is studied. We prove existence, uniqueness and time asymptotics for the solution. Furthermore, we study the plate equation with Dirichlet boundary condition. We give examples for right-hand sides f having unbounded support such that resonances occur.