The global profile of blow-up at space infinity in semilinear heat equations

Masahiko Shimojō

J. Math. Kyoto Univ., Tome 48 (2008) no. 4, p. 339-361 / Harvested from Project Euclid

Résumé

We consider semilinear heat equations on ${\mathbb{R}}^N$ and discuss the blow-up of solutions that occurs only at space infinity. We give sufficient conditions for such phenomena, and study the global profile of solutions at the blow-up time. Among other things, we establish a nearly optimal upper bound for the blow-up profile, which shows that the profile $u(x,T)$ cannot grow too fast as $|x|\to \infty$. We also prove that such blow-up is always complete.

Publié le : 2008-05-15
Classification:

@article{1250271415,
     author = {Masahiko Shimoj\=o},
     title = {The global profile of blow-up at space infinity in semilinear heat equations},
     journal = {J. Math. Kyoto Univ.},
     volume = {48},
     number = {4},
     year = {2008},
     pages = { 339-361},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250271415}
}

Masahiko Shimojō. The global profile of blow-up at space infinity in semilinear heat equations. J. Math. Kyoto Univ., Tome 48 (2008) no. 4, pp.  339-361. http://gdmltest.u-ga.fr/item/1250271415/