Analytically weak solutions to SPDEs with unbounded time-dependent differential operators and an application

TL;DR

This paper investigates analytically weak solutions for SPDEs with unbounded, time-dependent operators in Hilbert spaces, providing conditions for existence and uniqueness, motivated by applications in industrial mathematics.

Contribution

It introduces new conditions for the existence and uniqueness of analytically weak solutions to SPDEs with unbounded, time-dependent operators.

Findings

Established criteria for solution existence and uniqueness.

Applied results to a specific SPDE in industrial mathematics.

Enhanced understanding of weak solutions in complex stochastic systems.

Abstract

We analyze the concepts of analytically weak solutions of stochastic differential equations (SDEs) in Hilbert spaces with time-dependent unbounded operators and give conditions for existence and uniqueness of such solutions. Our studies are motivated by a stochastic partial differential equation (SPDE) arising in industrial mathematics.