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

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

2003-12-29

arxiv.org/abs/math-ph/0312072v1

Physics

Mathematical Physics

Scientific paper

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).

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