We study in this paper the global existence and exponential decay of solutions of the non-linear unidimensional wave equation with a viscoelastic boundary condition. We prove that the dissipation induced by the memory e!ect is strong enough to secure global estimates, which allow us to show existenc
Exponential decay for Kirchhoff wave equation with nonlocal condition in a noncylindrical domain
โ Scribed by J. Ferreira; J.M.L. Santos; M.P. Matos; W.D. Bastos
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 501 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0895-7177
No coin nor oath required. For personal study only.
โฆ Synopsis
In this paper, we prove the exponential decay as time goes to infinity of regular solutions of the problem for the Kirchhoff wave equation with nonlocal condition and weak damping /:
where Q is a noncylindrieal domain of IR n+l (n _> 1) with the lateral boundary E and a is a positive constant.
๐ SIMILAR VOLUMES
Here we are concerned about the stability of the solution of internally damped wave equation y Y s โฌ y q โฌ y X with small damping constant ) 0, in a bounded domain โ in R n under mixed undamped boundary conditions. A uniform expo-ลฝ . yโค t ลฝ . nential energy decay rate E t F Me E 0 where M G 1 and โค
The paper considers a particular type of closed-loop for the wave equation in one space dimension with damping acting at an arbitrary internal point, for which the uniform stabilization with exponential decay rate is shown. Applications to chains of coupled strings are also discussed.
## Abstract We study a decay property of solutions for the wave equation with a localized dissipation and a boundary dissipation in an exterior domain ฮฉ with the boundary โฮฉ = ฮ~0~ โช ฮ~1~, ฮ~0~ โฉ ฮ~1~ = โ ๏ธ. We impose the homogeneous Dirichlet condition on ฮ~0~ and a dissipative Neumann condition on
## Abstract This paper is concerned with some uniform energy decay estimates of solutions to the linear wave equations with strong dissipation in the exterior domain case. We shall derive the decay rate such as $(1+t)E(t)\le C$\nopagenumbers\end for some kinds of weighted initial data, where __E__(