Solution theory to semilinear parabolic stochastic partial differential equations with polynomially bounded coefficients

TL;DR

This paper establishes existence and uniqueness of function-valued solutions for a class of semilinear parabolic stochastic partial differential equations with polynomially bounded coefficients, under specific conditions on initial data and spectral measures.

Contribution

It introduces new conditions ensuring the existence and uniqueness of solutions for SPDEs with polynomially bounded operators, expanding the theoretical understanding of such equations.

Findings

Unique mild solutions exist under specified conditions

Conditions on initial data and spectral measures are established

Theoretical framework for semilinear SPDEs with polynomially bounded coefficients

Abstract

We study function-valued solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable parabolicity hypotheses. We provide conditions on the initial data and on the stochastic terms, namely, on the associated spectral measure, so that these mild solutions exist uniquely in suitably chosen functional classes.