Strong solutions for stochastic porous media equations with jumps

TL;DR

This paper establishes the existence and uniqueness of strong solutions for a class of stochastic porous media equations influenced by jump processes, advancing understanding of their mathematical properties.

Contribution

It introduces a novel proof of global well-posedness for stochastic porous media equations driven by jump martingales, extending previous results to more general stochastic influences.

Findings

Proved global existence and uniqueness of strong solutions.

Extended well-posedness results to equations with jump noise.

Provided a framework for analyzing stochastic porous media with jumps.

Abstract

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by square integrable martingales with stationary independent increments.