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On directional blow-up for quasilinear parabolic equations with fast diffusion. (English) Zbl 1144.35030
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.

35K55Nonlinear parabolic equations
35B40Asymptotic behavior of solutions of PDE
Full Text: DOI
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