Long time behavior for a semilinear hyperbolic equation with asymtotically vanishing damping term and convex potential
Analysis of PDEs
2014-12-23 v1
Abstract
We investigate the asymptotic behavior, as t goes to infinity, for a semilinear hyperbolic equation with asymptotically smal dissipation and convex potential. We prove that if the damping term behaves like K/t^\alpha for t large enough, k>0 and 0</alpha<1 then every global solution converges weakly to an equilibrium point. This result is a positive answer to a question left open in the paper [A. Cabot and P. Frankel, Asymptotics for some semilinear hyperbolic equation with non-autonomous damping. J. Differential Equations 252 (2012) 294-322.]
Keywords
Cite
@article{arxiv.1412.7008,
title = {Long time behavior for a semilinear hyperbolic equation with asymtotically vanishing damping term and convex potential},
author = {Ramzi May},
journal= {arXiv preprint arXiv:1412.7008},
year = {2014}
}
Comments
7 pages