Energy decay for damped wave equations on partially rectangular domains
نویسندگان
چکیده
We consider the wave equation with a damping term on a partially rectangular planar domain, assuming that the damping is concentrated close to the non-rectangular part of the domain. Polynomial decay estimates for the energy of the solution are established.
منابع مشابه
Energy decay for Maxwells equations with Ohms law in partially cubic domains
We prove a polynomial energy decay for the Maxwells equations with Ohms law in partially cubic domains with trapped rays. We extend the results of polynomial decay for the scalar damped wave equation in partially rectangular or cubic domain. Our approach have some similitude with the construction of reected gaussian beams. Keywords .Maxwells equations; decay estimates; trapped ray. 1 Introd...
متن کاملOn well-posedness and small data global existence for an interface damped free boundary fluid--structure model
We address a fluid–structure system which consists of the incompressible Navier–Stokes equations and a damped linear wave equation defined on two dynamic domains. The equations are coupled through transmission boundary conditions and additional boundary stabilization effects imposed on the free moving interface separating the two domains. Given sufficiently small initial data, we prove the glob...
متن کاملExponential decay of solutions of a nonlinearly damped wave equation
The issue of stablity of solutions to nonlinear wave equations has been addressed by many authors. So many results concerning energy decay have been established. Here in this paper we consider the following nonlinearly damped wave equation utt −∆u+ a(1 + |ut|)ut = bu|u|p−2, a, b > 0, in a bounded domain and show that, for suitably chosen initial data, the energy of the solution decays exponenti...
متن کاملExistence for Wave Equations on Domains with Arbitrary Growing Cracks
In this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations u...
متن کاملDecay of Solutions of the Wave Equation with Localized Nonlinear Damping and Trapped Rays
We prove some decay estimates of the energy of the wave equation governed by localized nonlinear dissipations in a bounded domain in which trapped rays may occur. The approach is based on a comparison with the linear damped wave equation and an interpolation argument. Our result extends to the nonlinear damped wave equation the well-known optimal logarithmic decay rate for the linear damped wav...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006