Mild Solutions and Harnack Inequality for Functional SPDEs with Dini Drift

TL;DR

This paper establishes the existence, uniqueness, and non-explosiveness of mild solutions for a class of functional SPDEs with Dini continuous drift and derives Harnack inequalities for their semigroups, extending known results.

Contribution

It proves the existence and uniqueness of solutions for functional SPDEs with Dini continuous drift and derives new Harnack inequalities even without delay.

Findings

Existence and uniqueness of mild solutions

Solutions are non-explosive under certain conditions

Harnack inequalities established for the semigroup

Abstract

The existence and uniqueness of the mild solution for a class of functional SPDEs with multiplicative noise and a locally Dini continuous drift are proved. In addition, under a reasonable condition the solution is non-explosive. Moreover, Harnack inequalities are derived for the associated semigroup under certain global conditions, which is new even in the case without delay.