Large-time behavior of solutions of parabolic equations on the real line with convergent initial data

Antoine Pauthier, Peter Poláčik

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We consider the semilinear parabolic equation ut = uxx + f(u) on the real line, where f is a locally Lipschitz function on R. We prove that if a solution u of this equation is bounded and its initial value u(x, 0) has distinct limits at x = ±∞ , then the solution is quasiconvergent, that is, all its limit profles as t → ∞ are steady states.

Original languageEnglish (US)
Pages (from-to)4423-4441
Number of pages19
JournalNonlinearity
Volume31
Issue number9
DOIs
StatePublished - Aug 7 2018

Bibliographical note

Funding Information:
1 Supported in part by the NSF Grant DMS-1565388.

Publisher Copyright:
© 2018 IOP Publishing Ltd & London Mathematical Society Printed in the UK.

Keywords

  • Parabolic equations on the real line
  • convergence
  • convergent initial data
  • quasiconvergence

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