On Instant Blow-up for Semilinear Heat Equations with Growing Initial Data
Giga, Yoshikazu ; Umeda, Noriaki
Methods Appl. Anal., Tome 15 (2008) no. 1, p. 185-196 / Harvested from Project Euclid
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For a semilinear heat equation admitting blow-up solutions a sufficient condition for nonexistence of local-in-time solutions are obtained. In particular, it is shown that if an initial data tends to infinity at space infinity then there is no local-in-time solution. As an application if the solution blows up at space infinity with least blow-up time, the solution cannot be extendable after blow-up time.
Publié le : 2008-06-15
Classification:  Instant blow-up,  local-in-time solution,  semilinear heat equation,  35K15,  35K55 
@article{1234536493,
     author = {Giga, Yoshikazu and Umeda, Noriaki},
     title = {On Instant Blow-up for Semilinear Heat Equations with Growing Initial Data},
     journal = {Methods Appl. Anal.},
     volume = {15},
     number = {1},
     year = {2008},
     pages = { 185-196},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1234536493}
}

Giga, Yoshikazu; Umeda, Noriaki. On Instant Blow-up for Semilinear Heat Equations with Growing Initial Data. Methods Appl. Anal., Tome 15 (2008) no. 1, pp.  185-196. http://gdmltest.u-ga.fr/item/1234536493/