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Selected Works of Luc Rey-Bellet
Article
Low regularity solutions to a gently stochastic nonlinear wave equation in nonequilibrium statistical mechanics
Stochastic Processes and their Applications (2005)
  • L Rey-Bellet, University of Massachusetts - Amherst
  • LE Thomas
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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
  • stochastic nonlinear wave equation,
  • Gibbs measures,
  • nonequilibrium statistical mechanics,
  • Hamiltonian PDE's,
  • low regularity solutions,
  • heat conduction
Disciplines
Publication Date
March, 2005
Publisher Statement
DOI: 10.1016/j.spa.2005.02.003
Citation Information
L Rey-Bellet and LE Thomas. "Low regularity solutions to a gently stochastic nonlinear wave equation in nonequilibrium statistical mechanics" Stochastic Processes and their Applications Vol. 115 Iss. 6 (2005)
Available at: http://works.bepress.com/luc_rey_bellet/2/