Distribution Dependent Stochastic Porous Media Equations

TL;DR

This paper establishes the existence and uniqueness of solutions for a class of distribution-dependent stochastic porous media equations using a generalized variational approach, extending classical results to more complex cases.

Contribution

It introduces a novel framework for analyzing distribution-dependent stochastic porous media equations, broadening the scope of well-posedness results in this area.

Findings

Proved strong and weak existence and uniqueness of solutions.

Extended classical well-posedness results to distribution-dependent cases.

Applied the framework to general measure spaces.

Abstract

Using the generalized variational framework, the strong/weak existence and uniqueness of solutions are derived for a class of distribution dependent stochastic porous media equations on general measure spaces, which also extends the classical well-posedness result of quasilinear SPDE to the distribution dependent case.