Low regularity solutions to a gently stochastic nonlinear wave equation in nonequilibrium statistical mechanics
Mathematical Physics
2007-05-23 v1 math.MP
Probability
Abstract
We consider a system of stochastic partial differential equations modeling heat conduction in a non-linear medium. We show global existence of solutions for the system in Sobolev spaces of low regularity, including spaces with norm beneath the energy norm. For the special case of thermal equilibrium, we also show the existence of an invariant measure (Gibbs state).
Keywords
Cite
@article{arxiv.math-ph/0312072,
title = {Low regularity solutions to a gently stochastic nonlinear wave equation in nonequilibrium statistical mechanics},
author = {Luc Rey-Bellet and Lawrence E. Thomas},
journal= {arXiv preprint arXiv:math-ph/0312072},
year = {2007}
}