The Dirichlet Problem for the Porous Medium Equation in Bounded Domains. Asymptotic Behavior

2004 ◽  
pp. 81-111 ◽  
Author(s):  
Juan Luis Vazquez
Keyword(s):  
Porous Medium ◽  
Asymptotic Behavior ◽  
Dirichlet Problem ◽  
Porous Medium Equation ◽  
Bounded Domains ◽  
Medium Equation

scholarly journals Near Field Asymptotic Behavior for the Porous Medium Equation on the Half-Line

2017 ◽  
Vol 17 (2) ◽  
Author(s):  
Carmen Cortázar ◽  
Fernando Quirós ◽  
Noemi Wolanski
Keyword(s):  
Porous Medium ◽  
Asymptotic Behavior ◽  
Near Field ◽  
Porous Medium Equation ◽  
Half Line ◽  
Medium Equation

AbstractKamin and Vázquez [

Complexity of asymptotic behavior of the porous medium equation in $${\mathbb{R}^N}$$

2011 ◽  
Vol 11 (2) ◽  
pp. 429-455 ◽  
Author(s):  
Jingxue Yin ◽  
Liangwei Wang ◽  
Rui Huang
Keyword(s):  
Porous Medium ◽  
Asymptotic Behavior ◽  
Porous Medium Equation ◽  
Medium Equation

scholarly journals A simple proof of the generalized Leibniz rule on bounded Euclidean domains

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Quoc-Hung Nguyen ◽  
Yannick Sire ◽  
Juan-Luis Vázquez
Keyword(s):  
Porous Medium ◽  
Partial Differential Equations ◽  
Simple Proof ◽  
Porous Medium Equation ◽  
Forthcoming Paper ◽  
Leibniz Rule ◽  
Bounded Domains ◽  
Medium Equation ◽  
Porous Medium Equations ◽  
Laplacian Equations

Abstract This paper is devoted to a simple proof of the generalized Leibniz rule in bounded domains. The operators under consideration are the so-called spectral Laplacian and the restricted Laplacian. Equations involving such operators have lately been considered by Constantin and Ignatova in the framework of the SQG equation [P. Constantin and M. Ignatova, Critical SQG in bounded domains, Ann. PDE 2 2016, 2, Article ID 8] in bounded domains, and by two of the authors [Q.-H. Nguyen and J. L. Vázquez, Porous medium equation with nonlocal pressure in a bounded domain, Comm. Partial Differential Equations 43 2018, 10, 1502–1539] in the framework of the porous medium with nonlocal pressure in bounded domains. We will use the estimates in this work in a forthcoming paper on the study of porous medium equations with pressure given by Riesz-type potentials.

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