On directional blow-up for quasilinear parabolic equations with fast diffusion

Yukihiro Seki

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18 Citations (Scopus)


We discuss blow-up at space infinity of solutions to quasilinear parabolic equations of the form ut = Δ φ{symbol} (u) + f (u) with initial data u0 ∈ L (RN), where φ{symbol} and f are nonnegative functions satisfying φ{symbol} ≤ 0 and ∫1 d ξ / f (ξ) < ∞. We study nonnegative blow-up solutions whose blow-up times coincide with those of solutions to the O.D.E. v = f (v) with initial data {norm of matrix} u0 {norm of matrix}L∞ (RN). We prove that such a solution blows up only at space infinity and possesses blow-up directions and that they are completely characterized by behavior of initial data. Moreover, necessary and sufficient conditions on initial data for blow-up at minimal blow-up time are also investigated.

Original languageEnglish
Pages (from-to)572-587
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - Feb 1 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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