Remarks on the method of modulus of continuity and the modified dissipative porous media equation

TL;DR

This paper uses Besov space techniques and the modulus of continuity method to establish the global well-posedness of a modified porous media equation, contributing to the mathematical understanding of such nonlinear PDEs.

Contribution

It introduces a novel approach combining Besov spaces and modulus of continuity to prove global well-posedness for the modified porous media equation.

Findings

Proved global existence and uniqueness of solutions.

Established regularity results for the modified equation.

Extended the applicability of modulus of continuity methods.

Abstract

We employ Besov space techniques and the method of modulus of continuity to obtain the global well-posedness of the modified Porous Media Equation.