A Liouville property and quasiconvergence for a semilinear heat equation

P. Poláčik, E. Yanagida

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31 Scopus citations


This paper is concerned with a supercritical semilinear diffusion equation with the power nonlinearity. Via establishing a Liouville-type property, we prove the quasiconvergence (convergence to a set of steady states) of a large class of global solutions. The method of proof relies on similarity variables and invariant manifold ideas.

Original languageEnglish (US)
Pages (from-to)194-214
Number of pages21
JournalJournal of Differential Equations
Issue number1 SPEC.ISS.
StatePublished - Jan 1 2005

Bibliographical note

Funding Information:
This work was supported in part by the Japan Society of Promotion of Science.


  • Liouville property
  • Quasiconvergence
  • Semilinear heat equation
  • Similarity variables


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