Porous medium equation with nonlocal pressure in a bounded domain

TL;DR

This paper investigates a broad class of nonlinear diffusive equations with nonlocal effects, specifically porous medium equations with fractional Laplacian pressure, on bounded domains, establishing existence, bounds, and regularity of solutions.

Contribution

It introduces the analysis of porous medium equations with fractional Laplacian pressure on bounded domains, providing existence and regularity results for weak solutions.

Findings

Existence of weak solutions established.

A priori bounds and regularity estimates derived.

Analysis extends porous medium equations to nonlocal fractional operators.

Abstract

We study a quite general family of nonlinear evolution equations of diffusive type with nonlocal effects. More precisely, we study porous medium equations with a fractional Laplacian pressure, and the problem is posed on a bounded space domain. We prove existence of weak solutions and suitable a priori bounds and regularity estimates.