Stochastic doubly nonlinear PDE: Large Deviation Principles and existence of Invariant measure

TL;DR

This paper proves large deviation principles for solutions of a stochastic doubly nonlinear PDE with multiplicative noise and demonstrates the existence of an invariant measure using probabilistic and analytical techniques.

Contribution

It introduces a novel approach combining monotonicity and weak convergence methods to analyze stochastic doubly nonlinear PDEs with multiplicative noise.

Findings

Established large deviation principles for the PDE solutions.

Proved existence of invariant probability measure.

Applied weak convergence and a-priori estimates in the analysis.

Abstract

In this paper, we establish large deviation principle for the strong solution of a doubly nonlinear PDE driven by small multiplicative Brownian noise. Motononicity arguments and the weak convergence approach have been exploited in the proof. Moreover, by using certain a-priori estimates and sequentially weakly Feller property of the associated Markov semigroup, we show existence of invariant probability measure for the strong solution of the underlying problem.