Let u be a type I blowing up solution of the Cauchy–Dirichlet problem for a semilinear heat equation, where Ω is a (possibly unbounded) domain in , , and . We prove that, if for some , then the blow-up set of the solution u is bounded. Furthermore, we give a sufficient condition for type I blowing up solutions not to blow up on the boundary of the domain Ω. This enables us to prove that, if Ω is an annulus, then the radially symmetric solutions of (P) do not blow up on the boundary ∂Ω.
@article{AIHPC_2014__31_2_231_0, author = {Fujishima, Yohei and Ishige, Kazuhiro}, title = {Blow-up set for type I blowing up solutions for a semilinear heat equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {31}, year = {2014}, pages = {231-247}, doi = {10.1016/j.anihpc.2013.03.001}, mrnumber = {3181667}, zbl = {1297.35052}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2014__31_2_231_0} }
Fujishima, Yohei; Ishige, Kazuhiro. Blow-up set for type I blowing up solutions for a semilinear heat equation. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) pp. 231-247. doi : 10.1016/j.anihpc.2013.03.001. http://gdmltest.u-ga.fr/item/AIHPC_2014__31_2_231_0/
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