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

Juan Luis Vázquez

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 3-4, page 281-300
  • ISSN: 1120-6330

Abstract

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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.

How to cite

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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. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 15.3-4 (2004): 281-300. <http://eudml.org/doc/252362>.

@article{Vázquez2004,
abstract = {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.},
author = {Vázquez, Juan Luis},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Blow-up; Semilinear heat equations; Thermal avalanche},
language = {eng},
month = {12},
number = {3-4},
pages = {281-300},
publisher = {Accademia Nazionale dei Lincei},
title = {The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation},
url = {http://eudml.org/doc/252362},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Vázquez, Juan Luis
TI - The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/12//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 3-4
SP - 281
EP - 300
AB - 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.
LA - eng
KW - Blow-up; Semilinear heat equations; Thermal avalanche
UR - http://eudml.org/doc/252362
ER -

References

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