A note on doubly nonlinear SPDEs with singular drift in divergence form

TL;DR

This paper establishes the well-posedness of a class of second-order stochastic partial differential equations with complex nonlinear drift and multiplicative noise, without imposing growth or continuity constraints.

Contribution

It introduces a novel framework for proving existence and uniqueness of solutions for SPDEs with doubly nonlinear divergence form and maximal monotone graphs.

Findings

Proved well-posedness for a broad class of SPDEs with singular drift.

Handled maximal monotone graphs without growth or continuity assumptions.

Extended the theory of SPDEs to include more general nonlinearities.

Abstract

We prove well-posedness for a class of second-order SPDEs with multiplicative Wiener noise and doubly nonlinear drift in divergence form involving maximal monotone graphs defined everywhere, on which neither growth nor continuity assumptions are imposed.