Boundary blow-up solutions for logistic-type porous media equations with nonregular source

Autores: Huiling Li, Peter Y. H. Pang, Mingxin Wang
Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 80, Nº 2, 2009, págs. 273-294
Idioma: inglés
DOI: 10.1112/jlms/jdp018
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Resumen
- In this paper, we establish the existence, uniqueness and blow-up rate near the boundary of boundary blow-up solutions to the porous media equations of logistic type .Äu = a(x)u1/m .
  
  b(x)f(u) with m > 1. We first consider the existence of such solutions for the general function f(u), and then study the uniqueness and the blow-up rate for the function f(u) whose variation at infinity is not regular. We also note the difference in the treatment of the blow-up rate for the cases where f varies regularly or not regularly at infinity.