On the equivalence of pathwise mild and weak solutions for quasilinear SPDEs

TL;DR

This paper establishes the equivalence between weak and pathwise mild solutions for parabolic quasilinear SPDEs, extending existing techniques from semilinear to quasilinear cases.

Contribution

It introduces a novel approach to relate weak and pathwise mild solutions specifically for quasilinear SPDEs, broadening the theoretical framework.

Findings

Proves the equivalence of weak and pathwise mild solutions for quasilinear SPDEs.

Extends techniques from semilinear to quasilinear SPDEs.

Provides a unified understanding of solution concepts in this context.

Abstract

The main goal of this work is to relate weak and pathwise mild solutions for parabolic quasilinear stochastic partial differential equations (SPDEs). Extending in a suitable way techniques from the theory of nonautonomous semilinear SPDEs to the quasilinear case, we prove the equivalence of these two solution concepts.