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Global existence, uniform decay and exponential growth for a class of semi-linear wave equation with strong damping

✍ Scribed by Hua CHEN; Gongwei LIU

Book ID
119528028
Publisher
Elsevier Science
Year
2013
Tongue
English
Weight
324 KB
Volume
33
Category
Article
ISSN
0252-9602

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πŸ“œ SIMILAR VOLUMES

Existence and uniform decay for a non-li
Existence and uniform decay for a non-linear viscoelastic equation with strong damping
✍ M. M. Cavalcanti; V. N. Domingos Cavalcanti; J. Ferreira πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 106 KB πŸ‘ 1 views

## 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 Ξ”__u~t~__ acting in the domain and provided the relaxation function decays exponentially.

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The goal of this paper is to study the global existence of small data solutions to the Cauchy problem for the nonlinear wave equation In particular we are interested in statements for the 1D case. We will explain how the interplay between the increasing and oscillating behavior of the coefficient w