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

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

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.

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