The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation

Vázquez, Juan Luis

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 15 (2004), p. 281-300 / Harvested from Biblioteca Digitale Italiana di Matematica

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Résumé

We review the main mathematical questions posed in blow-up problems for reaction-diffusion equations and discuss results of the author and collaborators on the subjects of continuation of solutions after blow-up, existence of transient blow-up solutions (so-called peaking solutions) and avalanche formation as a mechanism of complete blow-up.

Publié le : 2004-12-01

MR 2148886 | Zbl 1162.35392

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     author = {Juan Luis V\'azquez},
     title = {The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {15},
     year = {2004},
     pages = {281-300},
     zbl = {1162.35392},
     mrnumber = {2148886},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2004_9_15_3-4_281_0}
}

Vázquez, Juan Luis. The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 15 (2004) pp. 281-300. http://gdmltest.u-ga.fr/item/RLIN_2004_9_15_3-4_281_0/

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