Refined asymptotics for the blowup of ut — δu = up

Stathis Filippas, Robert V. Kohn

Research output: Contribution to journalArticle

Abstract

This work is concerned with positive, blowing‐up solutions of the semilinear heat equation ut — δu = up in Rn. Our main contribution is a sort of center manifold analysis for the equation in similarity variables, leading to refined asymptotics for u in a backward space‐time parabola near any blowup point. We also explore a connection between the asymptotics of u and the local geometry of the blowup set.

Original languageEnglish (US)
Pages (from-to)821-869
Number of pages49
JournalCommunications on Pure and Applied Mathematics
Volume45
Issue number7
DOIs
StatePublished - Aug 1992

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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