Quasilinear parabolic stochastic partial differential equations: existence, uniqueness

TL;DR

This paper establishes the existence and uniqueness of solutions for a class of quasilinear stochastic PDEs that lack monotonicity, using a direct analytical approach.

Contribution

It introduces a novel direct method to prove existence and uniqueness for non-monotone quasilinear stochastic PDEs.

Findings

Proved existence of strong and weak solutions.

Established uniqueness under non-monotonic conditions.

Provided a framework applicable to complex stochastic PDEs.

Abstract

In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone nor locally monotone.