Quasi-linear equations in Hilbert spaces and nonlinear random perturbations of PDEs

Guatteri giuseppina, Politecnico di Milano

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 semigroup associated with such equation, we then introduce the corresponding SPDE and we study the asymptotic behavior of its solutions, depending on the small parameter. Namely, we show that a large deviations principle holds and we give an explicit description of the action functional. This result is obtained in collaboration with S. Cerrai (University of Maryland) and G. Tessitore (University Milano Bicocca).

Area: CS16 - Stochastic Evolution Equations (Irene Benedetti)

Keywords: PDE in Hilbert spaces, SPDEs

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