Low regularity solutions to a gently stochastic nonlinear wave equation in nonequilibrium statistical mechanics

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:115

Article

Rey-Bellet, L ; Thomas, LE

关键词: stochastic nonlinear wave equation;    Gibbs measures;    nonequilibrium statistical mechanics;    Hamiltonian PDE's;    low regularity solutions;    heat conduction;   

DOI  :  10.1016/j.spa.2005.02.003

来源: Elsevier

【 摘 要 】

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). (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

Free