计算验证中各向异性抛物方程的可移性条件

Dirk Langemann, Mariia Savchenko
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摘要

文章研究了各向异性抛物方程,特别是各向异性多孔介质方程奇点的可移动性条件,旨在对分析结果进行数值验证。分析了各向异性强度的先决条件,并将奇点附近解增长行为的分析估计与数值模拟中观察到的增长进行了比较。尽管在证明中使用了经典估计值,但我们发现分析估计值与数值观测到的解行为惊人地接近。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Removability conditions for anisotropic parabolic equations in a computational validation
The article investigates removability conditions for singularities of anisotropic parabolic equations and in particular for the anisotropic porous medium equation and it aims in the numerical validation of the analytical results. The preconditions on the strength of the anisotropy are analyzed, and the analytical estimates for the growth behavior of the solutions near the singularities are compared with the observed growth in numerical simulations. Despite classical estimates used in the proof, we find that the analytical estimates are surprisingly close to the numerically observed solution behavior.
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