Nonlinear random perturbations of PDEs and quasi-linear equations in Hilbert spaces depending on a small parameter

2022/08/26 by Sandra Cerrai, Cerrai, Sandra, Giuseppina Guatteri +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2208.12867

openalex publication_date 2022/08/26 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28

Abstract

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 introduce the corresponding SPDE and we study the asymptotic behavior of its solutions, depending on the small parameter. We show that a large deviations principle holds and we give an explicit description of the action functional.

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