Asymptotic Behavior for a Strongly Damped Nonlinear Wave Equation.
Abstract
This paper is a specific application of the author's recent paper, on 'Limiting Behavior for Strongly Damped Nonlinear Wave Equations' where results of Webb and Fitzgibbon were extended by applying results of a few recent papers written by the author. Some of the main results of this paper are to show boundedness of orbits in one space implies boundedness of orbits in other spaces (the technique ehre provides an interesting alternative proof of the main results of Alikakos. Invariant sets in one space are automatically invariant sets in many spaces (which implies smoothness properties of invariant sets), point dissipative and compact dissipative are equivalent in many spaces and imply bounded dissipative in spaces of 'smoother' functions, the existence of a 'very smooth' maximal compact invariant set under a very weak dissipative assumption, along with its strong stability and attractivity properties in several spaces, and fixed point theorems under these weak dissipative hypotheses.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1980
- Accession Number
- ADA090548
Entities
People
- Paul Massatt
Organizations
- Brown University