We first consider the wave equation in an exterior domain Ω in RN with two separated boundary parts Γ0, Γ1. On Γ0, the Dirichlet condition u |Γ0 = 0 is imposed, while on Γ1, Neumann type nonlinear boundary dissipation ∂ u / ∂ ν = - g (ut) is assumed. Further, a 'half-linear' localized dissipation is attached on Ω. For such a situation we derive a precise rate of decay of the energy E (t) for solutions of the initial boundary value problem. We impose no geometrical condition on the shape of the boundary ∂ Ω = Γ0 ∪ Γ1. Secondly, when a T periodic forcing term works we prove the existence of a T periodic solution on R under an additional growth assumption on ρ (x, v) and g (v).
|ジャーナル||Nonlinear Analysis, Theory, Methods and Applications|
|出版ステータス||Published - 2007 1 15|
ASJC Scopus subject areas
- Applied Mathematics