Finite time extinction for solutions to fast diffusion stochastic porous media equations

TL;DR

This paper proves that solutions to fast diffusion stochastic porous media equations can completely vanish in finite time with positive probability, highlighting a significant extinction phenomenon in stochastic porous media models.

Contribution

It establishes the finite time extinction property for solutions to stochastic porous media equations with fast diffusion, a novel result in the stochastic PDE literature.

Findings

Solutions exhibit finite time extinction with positive probability.

The extinction phenomenon is rigorously proven for the stochastic model.

The result extends understanding of stochastic porous media dynamics.

Abstract

We prove that the solutions to fast diffusion stochastic porous media equations have finite time extinction with strictly positive probability.