scholarly journals Solutions of the One-Dimensional Porous Medium Equation are Determined by Their Free Boundary

1990 ◽  
Vol s2-42 (2) ◽  
pp. 339-353 ◽  
Author(s):  
Sigurd Angenent
Keyword(s):  
Porous Medium ◽  
Free Boundary ◽  
Porous Medium Equation ◽  
One Dimensional ◽  
Medium Equation ◽  
The One

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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