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Zbl 1106.35029
Giga, Yoshikazu; Umeda, Noriaki
On blow-up at space infinity for semilinear heat equations. (English)
[J] J. Math. Anal. Appl. 316, No. 2, 538-555 (2006). ISSN 0022-247X

Positive solutions of the Cauchy problem for a semilinear heat equation are studied. The authors give sufficient conditions under which the solutions blow up in finite time but the blow-up set is empty. This means that these solutions only become unbounded as $\vert x\vert \to\infty$. It is also shown in the paper that the behavior at spatial infinity is described by the corresponding ordinary differential equation.
[Marek Fila (Bratislava)]

MSC 2000:: *35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions of PDE

Keywords: semilinear heat equation; blow-up

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