Stable blow-up patterns

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45 Scopus citations


For the semilinear heat equation ut = Δu + eu in a convex domain Ω ⊂ Rn, given any b ε{lunate} Ω we show the existence of solutions which blow up in finite time exactly at b and whose final profile has the form u(T, x) ≈ -2 ln |x - b| + ln |ln |x - b|| + ln 8, T being the blow-up time. Using a suitable set of rescaled coordinates, this asymptotic behavior is proved to be stable with respect to small perturbations of the initial conditions.

Original languageEnglish (US)
Pages (from-to)57-75
Number of pages19
JournalJournal of Differential Equations
Issue number1
StatePublished - Jul 1992

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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