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

Zhanwei Gou; Jincheng Shi; Zhanwei Gou; Jincheng Shi

doi:10.3934/math.2023598

AIMS Mathematics

2023, Volume 8, Issue 5: 11822-11836. doi: 10.3934/math.2023598

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

Zhanwei Gou ^{1
,
,},
Jincheng Shi ²

1.
Basic Teaching Department, Guangdong Communication Polytechnic, Guangzhou 510650, China
2.
Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou 511300, China

Received: 25 August 2022 Revised: 01 March 2023 Accepted: 02 March 2023 Published: 20 March 2023
MSC : 35K55, 35K61

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 $.
- blow-up,
- lower bounds,
- higher dimensional spaces
Citation: Zhanwei Gou, Jincheng Shi. Blow-up phenomena and global existence for nonlinear parabolic problems under nonlinear boundary conditions[J]. AIMS Mathematics, 2023, 8(5): 11822-11836. doi: 10.3934/math.2023598

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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 $.

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