scholarly journals Large time behaviour of solutions of the porous medium equation in bounded domains

1981 ◽  
Vol 39 (3) ◽  
pp. 378-412 ◽  
Author(s):  
D.G Aronson ◽  
L.A Peletier
Keyword(s):  
Porous Medium ◽  
Large Time ◽  
Porous Medium Equation ◽  
Bounded Domains ◽  
Time Behaviour ◽  
Large Time Behaviour ◽  
Medium Equation

scholarly journals Large time behavior of a two phase extension of the porous medium equation

2019 ◽  
Vol 21 (2) ◽  
pp. 199-229 ◽  
Author(s):  
Ahmed Ait Hammou Oulhaj ◽  
Clément Cancès ◽  
Claire Chainais-Hillairet ◽  
Philippe Laurençot
Keyword(s):  
Porous Medium ◽  
Large Time ◽  
Porous Medium Equation ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Two Phase ◽  
Medium Equation ◽  
Phase Extension

Large time estimates for solutions to the porous medium equation with nonintegrable data via comparison

1985 ◽  
Vol 100 (1-2) ◽  
pp. 1-10
Author(s):  
Nicholas D. Alikakos ◽  
Rouben Rostamian
Keyword(s):  
Porous Medium ◽  
Initial Data ◽  
Original Problem ◽  
Large Time ◽  
Porous Medium Equation ◽  
Comparison Method ◽  
Upper And Lower Bounds ◽  
Medium Equation ◽  
Time Estimates ◽  
The Cauchy Problem

SynopsisWe consider the Cauchy problem for the porous medium equation in one space dimension, with initial data which are locally integrable. We measure the asymptotic behaviour of the initial data near infinity in an integral sense and relate this to the pointwise rate of growth or decay of solution for large time. The emphasis is on a novel comparison method wherein the initial data are rearranged on the ×-axis to form a sequence of Dirac δ-masses. By using the explicit solution in the latter case, we derive upper and lower bounds for the solution to the original problem by comparisons.

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.

scholarly journals Large time behavior for the porous medium equation with convection

Meccanica ◽  
2017 ◽  
Vol 52 (13) ◽  
pp. 3255-3260 ◽  
Author(s):  
Daniele Andreucci ◽  
Anatoli F. Tedeev
Keyword(s):  
Porous Medium ◽  
Large Time ◽  
Porous Medium Equation ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Medium Equation
Sign in / Sign up

Export Citation Format

Share Document