多孔介质方程在时间和空间上的最佳规律性

IF 1.9 1区数学 Q1 MATHEMATICS

Analysis & PDE Pub Date : 2019-02-22 DOI:10.2140/apde.2020.13.2441

B. Gess, J. Sauer, E. Tadmor

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引用次数: 14

摘要

多孔介质方程解在时间和空间上的正则性估计显示在Sobolev空间的尺度中。此外，还得到了解的幂的更高的空间正则性。标度论证表明这些估计是最优的。在线性极限中，已证明的正则性估计与线性情形的最优正则性是一致的。

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Optimal regularity in time and space for the porous medium equation

Regularity estimates in time and space for solutions to the porous medium equation are shown in the scale of Sobolev spaces. In addition, higher spatial regularity for powers of the solutions is obtained. Scaling arguments indicate that these estimates are optimal. In the linear limit, the proven regularity estimates are consistent with the optimal regularity of the linear case.

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来源期刊

Analysis & PDE MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： APDE aims to be the leading specialized scholarly publication in mathematical analysis. The full editorial board votes on all articles, accounting for the journal’s exceptionally high standard and ensuring its broad profile.