Strong solutions to semilinear SPDEs

TL;DR

This paper establishes the existence of strong solutions for semilinear stochastic partial differential equations driven by finite-dimensional Wiener processes, under smoothness and boundedness conditions on the coefficients, using semigroup methods.

Contribution

It provides a rigorous proof of strong solution existence for semilinear SPDEs with smooth coefficients in a power scale framework, extending previous results.

Findings

Existence of continuous strong solutions under specified conditions

Application of semigroup techniques to SPDEs

Framework applicable to equations with strongly elliptic operators

Abstract

We study the Cauchy problem for a semilinear stochastic partial differential equation driven by a finite-dimensional Wiener process. In particular, under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives, we consider the equation in the context of power scale generated by a strongly elliptic differential operator. Application of semigroup arguments then yields the existence of a continuous strong solution.