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SPDEs on narrow channels and graphs: convergence and large deviations in case of non smooth noise
Sandra Cerrai, Wen-Tai Hsu
We investigate a class of stochastic partial differential equations of reaction-diffusion type defined on graphs, which can be derived as the limit of SPDEs on narrow planar channe…
On the small-mass limit for stationary solutions of stochastic wave equations with state dependent friction
Sandra Cerrai, Mengzi Xie
We investigate the convergence, in the small mass limit, of the stationary solutions of a class of stochastic damped wave equations, where the friction coefficient depends on the s…
Nonlinear random perturbations of PDEs and quasi-linear equations in Hilbert spaces depending on a small parameter
Sandra Cerrai, Giuseppina Guatteri, Gianmario Tessitore
We study a class of quasi-linear parabolic equations defined on a separable Hilbert space, depending on a small parameter in front of the second order term. Through the nonlinear s…
Fast flow asymptotics for stochastic incompressible viscous fluids in and SPDEs on graphs
Sandra Cerrai, Mark Freidlin
Fast advection asymptotics for a stochastic reaction-diffusion-advection equation are studied in this paper. To describe the asymptotics, one should consider a suitable class of SP…
On the Smoluchowski-Kramers approximation for a system with infinite degrees of freedom exposed to a magnetic field
Sandra Cerrai, Michael Salins
We study the validity of the so-called Smoluchowski-Kramers approximation for a two dimensional system of stochastic partial differential equations, subject to a constant magnetic…
Smoluchowski-Kramers approximation and large deviations for infinite dimensional non-gradient systems with applications to the exit problem
Sandra Cerrai, Michael Salins
In this paper, we study the quasi-potential for a general class of damped semilinear stochastic wave equations. We show that, as the density of the mass converges to zero, the infi…