## Abstract This paper is concerned with the non‐linear viscoelastic equation We prove global existence of weak solutions. Furthermore, uniform decay rates of the energy are obtained assuming a strong damping Δ__u~t~__ acting in the domain and provided the relaxation function decays exponentially.
On the Existence and the Uniform Decay of a Hyperbolic Equation with Non-Linear Boundary Conditions
✍ Scribed by M. M. Cavalcanti; V. N. Domingos Cavalcanti; J. A. Soriano; L. A. Medeiros
- Publisher
- Springer
- Year
- 2000
- Weight
- 108 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0129-2021
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📜 SIMILAR VOLUMES
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
## Abstract In this paper we are concerned with the existence and energy decay of solution to the initial boundary value problem for the coupled Klein–Gordon–Schrödinger equations with non‐linear boundary damping and memory term. Copyright © 2006 John Wiley & Sons, Ltd.
We establish the existence of a global solution to an initial boundary value problem for the nonlinear anisotropic hyperbolic equation Depending on the range of the p i 's, we derive an exponential and a polynomial decay for the global solution.