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

Hongmei Li; Hongmei Li

doi:10.3934/math.2024140

AIMS Mathematics

2024, Volume 9, Issue 2: 2824-2853. doi: 10.3934/math.2024140

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Research article

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

Hongmei Li ^,

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

Received: 24 October 2023 Revised: 10 December 2023 Accepted: 12 December 2023 Published: 02 January 2024
MSC : 35B45, 35G30

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.
- convergence,
- uniformly parabolic equations,
- oblique derivative boundary condition,
- long time behavior,
- derivative estimates
Citation: Hongmei Li. Convergence of smooth solutions to parabolic equations with an oblique derivative boundary condition[J]. AIMS Mathematics, 2024, 9(2): 2824-2853. doi: 10.3934/math.2024140

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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.

References

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