Asymptotic properties of the stochastic heat equation in large times

TL;DR

This paper investigates the long-term behavior of solutions to the stochastic heat equation, providing insights into its asymptotic properties as time approaches infinity.

Contribution

It offers new theoretical analysis of the stochastic heat equation's asymptotic behavior, extending understanding of its long-term dynamics.

Findings

Characterization of the solution's asymptotic distribution

Conditions under which solutions stabilize or diverge

Insights into the influence of stochastic noise on long-term behavior

Abstract

In this article, we study the asymptotic behavior of the stochastic heat equation for large times.