Time-Dependent Attractor for the Oscillon Equation
Mathematical Physics
2010-09-15 v1 General Relativity and Quantum Cosmology
High Energy Physics - Theory
math.MP
Abstract
We investigate the asymptotic behavior of the nonautonomous evolution problem generated by the Klein-Gordon equation in an expanding background, in one space dimension with periodic boundary conditions, with a nonlinear potential of arbitrary polynomial growth. After constructing a suitable dynamical framework to deal with the explicit time dependence of the energy of the solution, we establish the existence of a regular, time-dependent global attractor. The sections of the attractor at given times have finite fractal dimension.
Cite
@article{arxiv.1009.2529,
title = {Time-Dependent Attractor for the Oscillon Equation},
author = {Francesco Di Plinio and Gregory S. Duane and Roger Temam},
journal= {arXiv preprint arXiv:1009.2529},
year = {2010}
}
Comments
to appear in Discrete and Continuous Dynamical Systems