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Luc Rey-Bellet and Lawrence E. Thomas
Low regularity solutions to a gently stochastic nonlinear wave equation in nonequilibrium statistical mechanics
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).