A note on stochastic semilinear dissipative evolution equations

TL;DR

This paper proves existence and uniqueness of mild solutions for a class of semilinear stochastic evolution equations with additive noise, where the linear part generates a compact semigroup and the nonlinear part is a decreasing superposition operator.

Contribution

It establishes well-posedness results for stochastic evolution equations with specific linear and nonlinear structures, extending previous theories.

Findings

Existence and uniqueness of solutions are proven.

The linear operator generates a compact semigroup.

The nonlinear part is a decreasing superposition operator.

Abstract

Existence and uniqueness of mild solutions to a class of semilinear stochastic evolution equations with additive noise is proved. The linear part of the drift term is the generator of a compact semigroup of contractions, while the nonlinear part is only assumed to be the superposition operator associated to a decreasing function.