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Smoluchowski-Kramers approximation for a general class of SPDEs

Authors:	Sandra Cerrai Mark Freidlin

Institution:	(1) Dip. di Matematica per le Decisioni, Università di Firenze, Via C. Lombroso 6/17, I-50134 Firenze, Italy;(2) Department of Mathematics, University of Maryland, College Park, Maryland, USA

Abstract:	We prove that the so-called Smoluchowski-Kramers approximation holds for a class of partial differential equations perturbed by a non-Gaussian noisy term. Namely, we show that the solution of the one-dimensional semi-linear stochastic damped wave equations $\mu u_{tt} (t,x) + u_{t} (t,x) = \Delta u(t,x) + b(x,u(t,x)) + g(x,u(t,x))\dot{w}(t)$ , u(0) = u₀, u_t (0) = v₀, endowed with Dirichlet boundary conditions, converges as the parameter μ goes to zero to the solution of the semi-linear stochastic heat equation $u_{t} (t,x) = \Delta u(t,x) + b(x,u(t,x)) + g(x,u(t,x))\dot{w}(t)$ , u(0) = u₀, endowed with Dirichlet boundary conditions. Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday

Keywords:	Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000)
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