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Research Article | Open Access

A Liouville-type theorem of a weighted semilinear parabolic equation on weighted manifolds with boundary

Junsheng Gong, Jiancheng Liu( )
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
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Abstract

We derive a Liouville-type theorem for positive ancient solutions to a weighted semilinear parabolic equation with a Dirichlet boundary condition on complete noncompact weighted manifolds with a compact boundary. This result can be viewed as an extension of Dung et al.'s work on a linear heat equation.

Keywords

Liouville-type theoremancient solutionsemilinear parabolic equationweighted manifoldgradient estimate

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Electronic Research Archive
Volume 33 Issue 4,
April 2025
Pages 2312-2324
DOI: 10.3934/era.2025102

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Gong J, Liu J. A Liouville-type theorem of a weighted semilinear parabolic equation on weighted manifolds with boundary. Electronic Research Archive, 2025, 33(4): 2312-2324. https://doi.org/10.3934/era.2025102

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Received: 18 January 2025
Revised: 30 March 2025
Accepted: 01 April 2025
Published: 15 April 2025
©2025 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)