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

School of 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

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Publisher Copyright:
© 2020 American Mathematical Society.

Keywords

Entire solutions
Liouville theorems
Semilinear parabolic equations
Zero number

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10.1090/proc/14978

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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.",

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AB - 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.

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KW - Zero number

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

Abstract

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Keywords

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