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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
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

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
Copyright
2002 Cambridge University Press

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