A new contraction family for porous medium and fast diffusion equation
Ghada Chmaycem (CERMICS), R\'egis Monneau (CERMICS), Mustapha Jazar
TL;DR
This paper introduces a novel two-dimensional contraction family for porous medium and fast diffusion equations, offering new a priori estimates that enhance understanding of solution behaviors, including for the standard heat equation.
Contribution
It presents a new contraction family approach that improves a priori estimates for porous medium and fast diffusion equations, including the classical heat equation.
Findings
Established a two-dimensional contraction family for these equations.
Provided improved a priori estimates for solutions.
Extended results to the standard heat equation.
Abstract
In this paper, we present a surprising two-dimensional contraction family for porous medium and fast diffusion equations. This approach provides new a priori estimates on the solutions, even for the standard heat equation.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Geometric Analysis and Curvature Flows