Rate of approach to a singular steady state in quasilinear reaction-diffusion equations

James W. Dold ^[1] ; Victor A. Galaktionov ^[2] ; Andrew A. Lacey ^[3] ; Juan Luis Vázquez ^[4]
1. [1] University of Manchester
  
  University of Manchester
  
  Reino Unido
2. [2] University of Bath
  
  University of Bath
  
  Reino Unido
3. [3] Heriot-Watt University
  
  Heriot-Watt University
  
  Reino Unido
4. [4] Universidad Autónoma de Madrid
  
  Universidad Autónoma de Madrid
  
  Madrid, España
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Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 26, Nº 4, 1998, págs. 663-687
Idioma: inglés
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Resumen
- We study the asymptotic behaviour of global-in-time sQlutions to a quasilinear reaction-diffusion equation in the case when it admits a unique stable stationary solution which is not a bounded function (a singular steady state). We investigate the convergence from below of global solutions to the singular state and discover that such a stabilization is not of a self-similar nature. Actually, it is given by a certain matching of different asymptotic developments in the large outer region closer to the boundary and the thin inner region near the singularity.