Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation
AUTOR(ES)
Barenblatt, G. I.
FONTE
The National Academy of Sciences
RESUMO
The equation ∂tu = u∂xx2u − (c − 1)(∂xu)2 is known in literature as a qualitative mathematical model of some biological phenomena. Here this equation is derived as a model of the groundwater flow in a water-absorbing fissurized porous rock; therefore, we refer to this equation as a filtration-absorption equation. A family of self-similar solutions to this equation is constructed. Numerical investigation of the evolution of non-self-similar solutions to the Cauchy problems having compactly supported initial conditions is performed. Numerical experiments indicate that the self-similar solutions obtained represent intermediate asymptotics of a wider class of solutions when the influence of details of the initial conditions disappears but the solution is still far from the ultimate state: identical zero. An open problem caused by the nonuniqueness of the solution of the Cauchy problem is discussed.
ACESSO AO ARTIGO
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=27602Documentos Relacionados
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