Ukrainian Mathematical Bulletin
Volume 1, Issue 4, 2004 pp. 587-600.
Blow-up Phenomena Arising in a Reaction-Absorption-Diffusion Equation with Gradient DiffusivityAuthors: Manuela Chaves
Author institution: Manuela Chaves, Departamento de Matem'aticas, Universidad Aut'onoma de Madrid, 28049 Madrid, Spain, manuela.chaves@uam.es
Summary: We study the blow-up phenomena arising in a $p$-laplacian equation with reaction and absorption terms. We show that there exists a unique blowing-up {\sl approximate self-similar solution} which describe the asymptotic singular behaviour of a wide class of solutions. As a consequence, we conclude that in this class, the absorption became negligible in finite time in the competition between the reaction and the absorption terms.
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