𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Exponential decay of non-linear wave equation with a viscoelastic boundary condition

✍ Scribed by Jaime E. Muñoz Rivera; Doherty Andrade

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
152 KB
Volume
23
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

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 existence of global smooth solution for small initial data. We also prove that the solution decays exponentially provided the resolvent kernel of the relaxation function, k decays exponentially. When k decays polynomially, the solution decays polynomially and with the same rate.

📜 SIMILAR VOLUMES

A non-linear parabolic control problem w
A non-linear parabolic control problem with non-homogeneous boundary condition—convergence of Galerkin approximation
✍ Anna Dębińska-Nagórska; Andrzej Just; Zdzisław Stempień 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 134 KB 👁 2 views

The paper is concerned with optimal control problem for a non-linear parabolic equation with nonhomogenous boundary condition and quadratic cost. The control is acting in a nonlinear equation. We derive some results on the existence of optimal controls. Then we treat optimal control problem by Galer

On Global Existence, Asymptotic Stabilit
On Global Existence, Asymptotic Stability and Blowing Up of Solutions for Some Degenerate Non-linear Wave Equations of Kirchhoff Type with a Strong Dissipation
✍ Kosuke Ono 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 335 KB 👁 2 views

We study on the initial-boundary value problem for some degenerate non-linear wave equations of Kirchhoff type with a strong dissipation: When the initial energy associated with the equations is non-negative and small, a unique (weak) solution exists globally in time and has some decay properties.