各向异性非局部扩散模型的分析:反常输运分数问题的适定性

IF 1.9 4区数学 Q1 MATHEMATICS

Numerical Mathematics-Theory Methods and Applications Pub Date : 2022-10-01 DOI:10.4208/nmtma.oa-2022-0001s

Marta D’Elia, Mamikon Gulian

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引用次数: 0

摘要

我们分析了一类各向异性非局部扩散方程的适定性。在统一非局部矢量微积分中建立了加权和非加权各向异性非局部扩散算子之间的等价性，并将此分析应用于一类分数阶算子，给出了相应各向异性异常扩散方程解的严格估计。进一步，我们将分析扩展到各向异性扩散-平流方程，并证明了分数阶$s∈[0.5,1]的适定性。$我们也给出了平流-扩散方程在溶质异常输运中的应用。

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Analysis of Anisotropic Nonlocal Diffusion Models: Well-Posedness of Fractional Problems for Anomalous Transport

We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus, we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation. Furthermore, we extend our analysis to the anisotropic diffusion-advection equation and prove well-posedness for fractional orders $s ∈ [0.5, 1).$ We also present an application of the advection-diffusion equation to anomalous transport of solutes.

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来源期刊

Numerical Mathematics-Theory Methods and Applications 数学-数学

CiteScore

2.80

自引率

7.70%

发文量

审稿时长

>12 weeks

期刊介绍： Numerical Mathematics: Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction, analysis and application of numerical methods for solving scientific and engineering problems. Important research and expository papers devoted to the numerical solution of mathematical equations arising in all areas of science and technology are expected. The journal originates from the journal Numerical Mathematics: A Journal of Chinese Universities (English Edition). NM-TMA is a refereed international journal sponsored by Nanjing University and the Ministry of Education of China. As an international journal, NM-TMA is published in a timely fashion in printed and electronic forms.