Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations

Thomas Bartsch, Peter Poláčik, Pavol Quittner

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We prove a Liouville type theorem for sign-changing radial solutions of a subcritical semilinear heat equation ut = Δu + |u| p-1u. We use this theorem to derive a priori bounds, decay estimates, and initial and final blow-up rates for radial solutions of rather general semilinear parabolic equations whose nonlinearities have a subcritical polynomial growth. Further consequences on the existence of steady states and time-periodic solutions are also shown.

Original languageEnglish (US)
Pages (from-to)219-247
Number of pages29
JournalJournal of the European Mathematical Society
Volume13
Issue number1
DOIs
StatePublished - 2011

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