Time asymptotics for the biharmonic wave equation in exterior domains

Article type: Research Article

Authors: Lesky, Peter H.

Affiliations: Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, D 70569 Stuttgart, Germany, E-mail: [email protected]

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.

DOI: 10.3233/ASY-1997-153-407

Journal: Asymptotic Analysis, vol. 15, no. 3-4, pp. 359-384, 1997