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

P. Poláčik

doi:10.1090/proc/14978

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

P. Poláčik

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 language	English (US)
Pages (from-to)	2997-3008
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	7
DOIs	https://doi.org/10.1090/proc/14978
State	Published - 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.

Publisher Copyright:
© 2020 American Mathematical Society.

Keywords

Entire solutions
Liouville theorems
Semilinear parabolic equations
Zero number

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

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