Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-19T09:30:45.813Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stability of a class of self-similar solutions to the filtration-absorption equation

Published online by Cambridge University Press:  16 April 2002

ALINA CHERTOCK
ALINA CHERTOCK
Affiliation:
Department of Mathematics, University of California and Lawrence Berkeley National Laboratory, MS 50A-1148, 1 Cyclotron Rd, Berkeley, CA 94720, USA email: alina@math.lbl.gov
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the one-dimensional and two-dimensional filtration-absorption equation ut = uΔu−(c−1)(∇u)2. The one-dimensional case was considered previously by Barenblatt et al. [4], where a special class of self-similar solutions was introduced. By the analogy with the 1D case we construct a family of axisymmetric solutions in 2D. We demonstrate numerically that the self-similar solutions obtained attract the solutions of non-self-similar Cauchy problems having the initial condition of compact support. The main analytical result we provide is the linear stability of the above self-similar solutions both in the 1D case and in the 2D case.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 13 , Issue 2 , April 2002 , pp. 179 - 194
Copyright
2002 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)