scholarly journals Long time behaviour for a diffusion process associated with a porous medium equation

1995 ◽  
Vol 25 (1) ◽  
pp. 159-170
Author(s):  
Masaaki Inoue
Keyword(s):  
Porous Medium ◽  
Diffusion Process ◽  
Porous Medium Equation ◽  
Time Behaviour ◽  
Medium Equation ◽  
Long Time Behaviour ◽  
Long Time

Long-time behaviour for porous medium equations with convection

1998 ◽  
Vol 128 (2) ◽  
pp. 315-336 ◽  
Author(s):  
Ph. Laurençot ◽  
F. Simondon
Keyword(s):  
Porous Medium ◽  
Real Line ◽  
Integrable Function ◽  
Time Profile ◽  
Decay Estimates ◽  
Time Behaviour ◽  
Temporal Decay ◽  
Long Time Behaviour ◽  
Long Time ◽  
Porous Medium Equations

Long-time behaviour of solutions to porous medium equations with convection is investigated when the initial datum is a non-negative and integrable function on the real line. The long-time profile of the solutions is determined, and depends on whether the convective or the diffusive effect dominates for large times. Sharp temporal decay estimates are also provided.

The long-time behaviour of the thermoconvective flow in a porous medium

2004 ◽  
Vol 27 (8) ◽  
pp. 907-930 ◽  
Author(s):  
M. A. Efendiev ◽  
J. Fuhrmann ◽  
S. V. Zelik
Keyword(s):  
Porous Medium ◽  
Time Behaviour ◽  
Long Time Behaviour ◽  
Long Time

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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