A blowing up solution of the semilinear heat equation u_t = \Delta u+f(u) with f satisfying lim inf f(u)=u^p > 0 for some p > 1 is considered when initial data u_0 satisfies u_0 \leq M, u\ne M and lim_{m\rightarrow infity} inf_{x\in B_m} u_0(x) = M with sequence of ball {B_m} whose radius diverging to infinity. It is shown that the solution blows up only at space infinity. A notion of blow-up direction is introduced. A characterization for blow-up direction is also established.
@article{7450,
title = {Blow-up directions at space infinity for solutions of semilinear heat equations - doi: 10.5269/bspm.v23i1-2.7450},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {23},
year = {2009},
doi = {10.5269/bspm.v23i1-2.7450},
language = {EN},
url = {http://dml.mathdoc.fr/item/7450}
}
Umeda, Noriaki; Giga, Yoshikazu. Blow-up directions at space infinity for solutions of semilinear heat equations - doi: 10.5269/bspm.v23i1-2.7450. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v23i1-2.7450. http://gdmltest.u-ga.fr/item/7450/