Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption

• Autores: Jesús Ildefonso Díaz Díaz, José Evaristo Saa Requejo
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 36, Nº 1, 1992, págs. 19-38
• Idioma: inglés
• Títulos paralelos:
  • Unicidad de la solución auto-semejante muy singular de una ecuación parabólica degenerada cuasi-lineal con absorción
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• Resumen

  • We show the uniqueness of the very singular self-similar solution of the equation ut - ? pum + uq = 0.

    The result is carried out by studying the stationary associate equation and by introducing a suitable change of unknown. That allows to assume the zero-order perturbation term in the new equation to be monotone increasing. A careful study of the behaviour of solutions near the boundary of their support is also used in order to prove the main result.