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Zbl 1144.35030
Seki, Yukihiro
On directional blow-up for quasilinear parabolic equations with fast diffusion. (English)
[J] J. Math. Anal. Appl. 338, No. 1, 572-587 (2008). ISSN 0022-247X

Blow-up of positive solutions of the Cauchy problem for a quasilinear parabolic equation of the fast diffusion type is studied. It is shown that if a solution blows up at minimal blow-up time then it blows up only at space infinity and possesses blow-up directions which are characterized by initial data. A necessary and sufficient condition for blow-up at minimal blow-up time is also given.
[Marek Fila (Bratislava)]
MSC 2000:
*35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions of PDE

Keywords: blow-up at space infinity; blow-up direction; minimal blow-up time

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