Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation

• DOI: 10.1073/pnas.97.18.9844
• Publication Date: 2002-07-26T14:40:52Z
• Authors: G. I. Barenblatt; M. Bertsch; A. E. Chertock; V. M. Prostokishin
• Keywords: Filtration (mathematics)

The equation ∂ t u = u∂ xx 2 − ( c 1)(∂ x ) is known in literature as a qualitative mathematical model of some biological phenomena. Here this derived the groundwater flow water-absorbing fissurized porous rock; therefore, we refer to filtration-absorption equation. A family self-similar solutions constructed. Numerical investigation evolution non-self-similar Cauchy problems having compactly supported initial conditions performed. experiments indicate that obtained represent intermediate asymptotics wider class when influence details disappears but solution still far from ultimate state: identical zero. An open problem caused by nonuniqueness discussed.