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Smoluchowski-Kramers approximation and large deviations for the stochastic wave equation

Spring 2016
Seminar Date: 
Monday, April 25 1:30pm - 6:15pm at Brown
Mickey Salins (Boston University)

The motion of a vibrating material that is exposed to both deterministic and random forcing can be described by the damped semi-linear stochastic wave equation. As the mass density of the material converges to zero, the solutions of the damped semi-linear stochastic wave equations converge to the solution of a semi-linear stochastic heat equation uniformly on finite time intervals. This is called the Smoluchowski-Kramers approximation. In this talk, we compare the large deviations behaviors of the stochastic wave equations and the stochastic heat equations in the context of exit problems from a domain of attraction in the small noise regime. Despite the fact that the solutions of the stochastic wave equations are not pathwise close to the solutions stochastic heat equation on long time scales, these results show that the Smoluchowski-Kramers approximation is valid for approximating some long-time behaviors including exit times and exit solutions.