Stochastic Porous Media Equation and Self-Organized Criticality
Viorel Barbu (Institute of Mathematics "Octav Mayer", Iasi, Romania),, Giuseppe Da Prato (Scuola Normale Superiore di Pisa, Italy), Michael, R\"ockner (Faculty of Mathematics, Bielefeld, Germany, Departments of, Mathematics, Statistics, Purdue University, USA)
TL;DR
This paper proves the existence, uniqueness, and finite time extinction of solutions for stochastic porous media equations, highlighting their relevance to self-organized criticality in stochastic nonlinear diffusion systems.
Contribution
It establishes the first rigorous results on solutions for stochastic porous media equations with noncoercive diffusivity and connects these to self-organized critical phenomena.
Findings
Existence and uniqueness of solutions proven.
Finite time extinction with high probability in 1-D.
Relevance to self-organized criticality demonstrated.
Abstract
The existence and uniqueness of nonnegative strong solutions for stochastic porous media equations with noncoercive monotone diffusivity function and Wiener forcing term is proven. The finite time extinction of solutions with high probability is also proven in 1-D. The results are relevant for self-organized critical behaviour of stochastic nonlinear diffusion equations with critical states.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.