Geodesic
The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 3-4, pp. 281-300.

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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. 
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Vázquez, Juan Luis. The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 3-4, pp. 281-300. http://geodesic.mathdoc.fr/item/RLIN_2004_9_15_3-4_a10/

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