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Non-Euclidean distance fundamental solution of Hausdorff derivative partial differential equations

机译：Hausdorff偏微分方程的非欧式距离基本解

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摘要

The Hausdorff derivative partial differential equations have in recent years been found to be capable of describing complex mechanics and physics behaviors such as anomalous diffusion, creep and relaxation in fractal media. But most research is concerned with time Hausdorff derivative models, and little has been reported on the numerical solution of spatial Hausdorff derivative partial differential equations. In this study, we derive the fundamental solutions of the Hausdorff derivative Laplace, Helmholtz, modified Hemholtz, and convection-diffusion equations via a non-Euclidean metric, called the Hausdorff fractal distance. And then the singular boundary method is used to numerically simulate the steady heat transfer governed by the Hausdorff Laplace equation in comparison with the corresponding fractional Laplacian models. Numerical experiments show the validity and applicability of the derived fundamental solution of the Hausdorff Laplace equation.
机译：近年来，已发现Hausdorff导数偏微分方程能够描述复杂的力学和物理学行为，例如在分形介质中的异常扩散，蠕变和松弛。但是，大多数研究与时间Hausdorff导数模型有关，关于空间Hausdorff导数偏微分方程的数值解的报道很少。在这项研究中，我们通过称为Hausdorff分形距离的非欧氏度量推导出Hausdorff导数拉普拉斯，亥姆霍兹，修正的Hemholtz和对流扩散方程的基本解。然后，将奇异边界方法与相应的分数拉普拉斯模型进行比较，以数值模拟由Hausdorff Laplace方程控制的稳态传热。数值实验表明了Hausdorff Laplace方程的基本解的有效性和适用性。

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  • 来源
    《Engineering analysis with boundary elements》 |2017年第11期|213-219|共7页
  • 作者

    Wen Chen; Fajie Wang; Bin Zheng; Wei Cai;

  • 作者单位

    State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 210098, China;

    State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 210098, China;

    State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 210098, China;

    College of Mechanical and Electrical Engineering, Hohai University, Changzhou 213022, China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Non-Euclidean metric; Hausdorff fractal distance; Fractal; Fundamental solution; Singular boundary method; Hausdorff derivative;

    机译：非欧几里德度量;Hausdorff分形距离;分形基本解决方案;奇异边界法Hausdorff导数;

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