Metastability for parabolic equations with drift: part II. The quasilinear case

TL;DR

This paper investigates the metastability phenomena in quasi-linear parabolic equations with drift, extending previous work to provide a comprehensive PDE-based analysis of their long-term behavior.

Contribution

It offers a self-contained PDE approach to metastability in quasi-linear parabolic equations with drift, building upon and extending prior stochastic perturbation results.

Findings

Characterization of metastability in quasi-linear PDEs with drift

Extension of previous stochastic results to PDE framework

Detailed analysis of long-term solution behavior

Abstract

This is the second part of our series of papers on metastability results for parabolic equations with drift. The aim is to present a self-contained study, using partial differential equations methods, of the metastability properties of quasi-linear parabolic equations with a drift and to obtain results similar to those in Freidlin and Koralov [Nonlinear stochastic perturbations of dynamical systems and quasi-linear parabolic PDE's with a small parameter, Probab. Theory Related Fields 147 (2010), ArXiv:0903.0428v2 (2012)].