University of Toronto
               PDE/Applied Math/Analysis Seminar
                 Monday October 24, 3:10-4pm
                       1230 Bahen Center      




SPEAKER:  Lawrence E. Thomas (University of Virginia)

TITLE:    Stochastic differential equation models for heat
          flow in non-equilibrium statistical mechanics

ABSTRACT: We consider two systems modeling heat conduction 
          in a medium --- a non-linear system of stochastic 
          differential equations, and a system of 
          stochastic partial differential equations (a 
          stochastically driven non-linear wave equation 
          with dissipation). For these systems, we discuss 
          existence of invariant measures (stationary 
          states), which serve to describe steady-state 
          heat flow.

          Much of the talk will be concerned with the 
          wave equation system. We show global existence 
          of solutions in Sobolev spaces of low 
          regularity, including spaces with norm beneath 
          the energy norm. For the special case of thermal 
          equilibrium (no heat flow) we have existence 
          of an invariant measure (Gibbs state). For the 
          non-equilibrium case (with heat flow) we have 
          existence of invariant measures assuming certain 
          ultraviolet cut-offs. For the invariant measure
          of the corresponding linear wave equation system
          in non-equilibrium, we discuss sample space 
          properties of field configurations.

          (Joint work with Luc Rey-Bellet and Yao Wang.)







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University of Toronto PDE/Applied Math/Analysis Seminar 
http://www.math.toronto.edu/appmath/

2005-2006 organizers:
          Pieter Blue           pblue@ math.toronto.edu
          Almut Burchard        almut@ math.toronto.edu
          Bob Jerrard           rjerrard@ math.toronto.edu
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