Self-Similar Intermediate Asymptotics for a Degenerate Parabolic Filtration-Absorption Equation
Barenblatt, G. I. ; Bertsch, M. ; Chertock, A. E. ; Prostokishin, V. M.
arXiv, 0006008 / Harvested from arXiv
Text on arXiv
The equation $$ \partial_tu=u\partial^2_{xx}u-(c-1)(\partial_xu)^2 $$ 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.
Publié le : 2000-06-08
Classification:  Mathematical Physics 
@article{0006008,
     author = {Barenblatt, G. I. and Bertsch, M. and Chertock, A. E. and Prostokishin, V. M.},
     title = {Self-Similar Intermediate Asymptotics for a Degenerate Parabolic
  Filtration-Absorption Equation},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0006008}
}

Barenblatt, G. I.; Bertsch, M.; Chertock, A. E.; Prostokishin, V. M. Self-Similar Intermediate Asymptotics for a Degenerate Parabolic
  Filtration-Absorption Equation. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0006008/