Blow-up set for type I blowing up solutions for a semilinear heat equation
Yohei Fujishima
Division of Mathematical Science, Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, Toyonaka 560-8531, JapanKazuhiro Ishige
Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan
![Blow-up set for type I blowing up solutions for a semilinear heat equation cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-aihpc-volume-31-issue-2.png&w=3840&q=90)
Abstract
Let be a type I blowing up solution of the Cauchy–Dirichlet problem for a semilinear heat equation,
where 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 . This enables us to prove that, if is an annulus, then the radially symmetric solutions of () do not blow up on the boundary .
Cite this article
Yohei Fujishima, Kazuhiro Ishige, Blow-up set for type I blowing up solutions for a semilinear heat equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 2, pp. 231–247
DOI 10.1016/J.ANIHPC.2013.03.001