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Research Article | Open Access

A triviality result for semilinear parabolic equations

Daniele Castorina1, Giovanni Catino2, Carlo Mantegazza1( )
Dipartimento di Matematica e Applicazioni, Università di Napoli, Via Cintia, Monte S. Angelo 80126 Napoli, Italy
Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy
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Abstract

We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation

u t = Δ u + | u | p

on complete Riemannian manifolds of dimension n ≥ 5 with nonnegative Ricci tensor, when p is smaller than the critical Sobolev exponent n + 2 n − 2 .

Keywords

ancient solutioneternal solutionsuperlinear heat equation

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Mathematics in Engineering
Volume 4 Issue 1,
February 2022
Pages 1-15
DOI: 10.3934/mine.2022002

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Cite this article:
Castorina D, Catino G, Mantegazza C. A triviality result for semilinear parabolic equations. Mathematics in Engineering, 2022, 4(1): 1-15. https://doi.org/10.3934/mine.2022002

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Received: 15 July 2020
Accepted: 30 January 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)