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

Autor: Hongmei Li
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: AIMS Mathematics, Vol 9, Iss 2, Pp 2824-2853 (2024)
Druh dokumentu: article
ISSN: 2473-6988
DOI: 10.3934/math.2024140?viewType=HTML
Popis: 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.
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