Entire solutions and a liouville theorem for a class of parabolic equations on the real line

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Abstract

We consider a class of semilinear heat equations on ℝ, including in particular the Fujita equation (Equation presented) where p > 1. We first give a simple proof and an extension of a Liouville theorem concerning entire solutions with finite zero number. Then we show that there is an infinite-dimensional set of entire solutions with infinite zero number.

Original languageEnglish (US)
Pages (from-to)2997-3008
Number of pages12
JournalProceedings of the American Mathematical Society
Volume148
Issue number7
DOIs
StatePublished - Jul 2020

Bibliographical note

Funding Information:
Received by the editors June 18, 2018, and, in revised form, November 25, 2019. 2010 Mathematics Subject Classification. Primary 35K57, 35B40, 35B05. Key words and phrases. Semilinear parabolic equations, entire solutions, Liouville theorems, zero number. This research was supported in part by NSF Grant DMS-1565388.

Keywords

  • Entire solutions
  • Liouville theorems
  • Semilinear parabolic equations
  • Zero number

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