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Research Article | Open Access

Convergence of smooth solutions to parabolic equations with an oblique derivative boundary condition

School of Mathematics and Statistics, Taishan University, Taian, 271000, Shandong Province, China
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Abstract

In this paper, the parabolic equation with oblique derivative boundary condition is considered. The long time behavior of the solution is derived by selecting the appropriate auxiliary functions and making priori estimates. Through blow up analysis, time-dependent gradient estimates are obtained, followed by second-order derivative estimates. Then, the convergence of smooth solution to parabolic equations with the oblique derivative boundary condition is obtained using standard theory.

Keywords

convergenceuniformly parabolic equationsoblique derivative boundary conditionlong time behaviorderivative estimates
CLC number: 35B45, 35G30

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AIMS Mathematics
Volume 9 Issue 2,
February 2024
Pages 2824-2853
DOI: 10.3934/math.2024140

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Li H. Convergence of smooth solutions to parabolic equations with an oblique derivative boundary condition. AIMS Mathematics, 2024, 9(2): 2824-2853. https://doi.org/10.3934/math.2024140

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Received: 24 October 2023
Revised: 10 December 2023
Accepted: 12 December 2023
Published: 15 February 2024
©2024 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)