Nonlinear Random Perturbations of PDEs and Quasi-Linear Kolmogorov Equations in Hilbert Spaces

Giuseppina Guatteri (Politecnico Milano)

Feb 13. 2024, 14:00 — 14:40

We study random nonlinear perturbations of a PDE and prove that a large deviation principle holds. To this purpose we introduce 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. Studying the nonlinear semigroup associated with such equation, we are able to find sufficient regular solutions to derive the large deviations principle and  we give also an explicit description of the action functional, as in the finite dimensional case. This result is obtained in collaboration with S. Cerrai (University of Maryland) and G. Tessitore (University Milano Bicocca).

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Stochastic Partial Differential Equations (Workshop)
Organizer(s):
Sandra Cerrai (U of Maryland)
Martin Hairer (Imperial College London)
Carlo Marinelli (University College London)
Eulalia Nualart (U Barcelona)
Luca Scarpa (Politecnico Milano)
Ulisse Stefanelli (U of Vienna)