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.