Metastability for Non-Linear Random Perturbations of Dynamical Systems

TL;DR

This paper investigates the long-term behavior of solutions to quasi-linear parabolic equations with small perturbations and the associated diffusion processes, providing insights into metastability phenomena in nonlinear stochastic systems.

Contribution

It offers a novel analysis of metastability in nonlinear random perturbations of dynamical systems, connecting PDE solutions with stochastic process behavior over extended periods.

Findings

Characterization of metastable states in nonlinear systems

Asymptotic behavior of solutions as perturbation parameter approaches zero

Link between PDE solutions and diffusion process dynamics

Abstract

In this paper we describe the long time behavior of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion processes.