scholarly journals A probabilistic algorithm approximating solutions of a singular PDE of porous media type

2011 ◽  
Vol 17 (4) ◽  
Author(s):  
Nadia Belaribi ◽  
François Cuvelier ◽  
Francesco Russo
Keyword(s):  
Porous Media ◽  
Probabilistic Algorithm ◽  
Media Type ◽  
Singular Pde

scholarly journals Pattern formation in a flux limited reaction–diffusion equation of porous media type

2016 ◽  
Vol 206 (1) ◽  
pp. 57-108 ◽  
Author(s):  
J. Calvo ◽  
J. Campos ◽  
V. Caselles ◽  
O. Sánchez ◽  
J. Soler
Keyword(s):  
Porous Media ◽  
Pattern Formation ◽  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Media Type

A MATHEMATICAL ANALYSIS OF A MINIMAL MODEL OF NEMATODE MIGRATION IN SOIL

2002 ◽  
Vol 10 (01) ◽  
pp. 15-32 ◽  
Author(s):  
D. L. FELTHAM ◽  
M. A. J. CHAPLAIN ◽  
I. M. YOUNG ◽  
J. W. CRAWFORD
Keyword(s):  
Porous Media ◽  
Steady State ◽  
Experimental Work ◽  
Mathematical Analysis ◽  
Minimal Model ◽  
Large Time ◽  
Chemical Gradient ◽  
Media Type ◽  
Numerical Integrations ◽  
Analytical Results

A minimal model of nematode migration through soil in response to a chemical gradient is presented. We consider Fickian, fractal and porous-media type diffusion of the nematodes, for which the steady-state nematode distributions are found to compare favourably with experimental observations. Analytical results for Fickian nematode diffusion are presented, which are appropriate for the small- and large-time evolution of a nematode distribution. Numerical integrations allow us to compare the three types of nematode diffusion, to provide numerical validation of our analytical results, and to investigate the dependence of the results of our model upon certain key parameters. We conclude with a summary of results and a call for further experimental work.

Global solutions to norm-preserving non-local flows of porous media type

2013 ◽  
Vol 143 (4) ◽  
pp. 871-880
Author(s):  
Li Ma ◽  
Liang Cheng
Keyword(s):  
Porous Media ◽  
Compact Riemannian Manifold ◽  
Global Solutions ◽  
Local Heat ◽  
Cauchy Data ◽  
Laplacian Operator ◽  
Media Type ◽  
Existence Of Positive Solutions ◽  
Non Local ◽  
Image Position

In this paper, we study the global existence of positive solutions to the norm-preserving non-local heat flow of the porous-media type equations on the compact Riemannian manifold (M, g) with the Cauchy data u0 > 0 on M, where r ≥ 1, p > 1 and λ(t) is chosen to make the L2-norm of the solution u (or a power of u) constant. We show that the limit is an eigenfunction for the Laplacian operator. We use some tricky estimates through the Sobolev imbedding theorem and the Moser iteration method.

scholarly journals Probabilistic representation for solutions of an irregular porous media type equation

2010 ◽  
Vol 38 (5) ◽  
pp. 1870-1900 ◽  
Author(s):  
Philippe Blanchard ◽  
Michael Röckner ◽  
Francesco Russo
Keyword(s):  
Porous Media ◽  
Type Equation ◽  
Probabilistic Representation ◽  
Media Type
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