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Research Article | Open Access

Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions

Zhanwei Gou1( ), Jincheng Shi2
Basic Teaching Department, Guangdong Communication Polytechnic, Guangzhou 510650, China
Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China
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Abstract

In this paper, we consider an initial-boundary value parabolic problem under nonlinear Neumann boundary conditions. By virtue of the modified differential inequality, lower bounds for the blow-up time of the solution are derived in higher dimensional spaces. An upper bound for the blow-up time are specified under appropriate assumptions on the functions a , b , f , g , h and u 0 .

Keywords

blow-uplower boundshigher dimensional spaces
CLC number: 35K55, 35K61

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AIMS Mathematics
Volume 8 Issue 5,
May 2023
Pages 11822-11836
DOI: 10.3934/math.2023598

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Cite this article:
Gou Z, Shi J. Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions. AIMS Mathematics, 2023, 8(5): 11822-11836. https://doi.org/10.3934/math.2023598

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Received: 25 August 2022
Revised: 01 March 2023
Accepted: 02 March 2023
Published: 15 May 2023
©2023 the Author(s), licensee AIMS Press.

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