scholarly journals Long time existence of smooth solution for the porous medium equation in a bounded domain

2014 ◽  
Vol 267 (4) ◽  
pp. 1256-1284 ◽  
Author(s):  
Sunghoon Kim
Keyword(s):  
Porous Medium ◽  
Bounded Domain ◽  
Smooth Solution ◽  
Porous Medium Equation ◽  
Medium Equation ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence

scholarly journals Long-time asymptotics for a 1D nonlocal porous medium equation with absorption or convection

2019 ◽  
Vol 22 (03) ◽  
pp. 1950015
Author(s):  
Filomena Feo ◽  
Yanghong Huang ◽  
Bruno Volzone
Keyword(s):  
Porous Medium ◽  
Exponential Convergence ◽  
Porous Medium Equation ◽  
Entropy Method ◽  
Nonlocal Diffusion ◽  
One Dimensional ◽  
Medium Equation ◽  
Long Time ◽  
Porous Medium Equations ◽  
Long Time Asymptotics

In this paper, the long-time asymptotic behaviors of one-dimensional porous medium equations with a fractional pressure and absorption or convection are studied. In the parameter regimes when the nonlocal diffusion is dominant, the entropy method is adapted to derive the exponential convergence of relative entropy of solutions in similarity variables.

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