Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation.
The equation partial differential(t)u = u partial differential(xx)(2)u -(c-1)( partial differential(x)u)(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.
Barenblatt
G I
GI
Department of Mathematics and, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA.
Bertsch
M
M
Chertock
A E
AE
Prostokishin
V M
VM
D055593:Geological Phenomena; D005844:Geology; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D014867:Water
D014867:Water