纯分数阶riesz引力场局部涨落方程的极大值原理

V. Litovchenko
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引用次数: 0

摘要

具有Riesz分数阶微分算子的抛物型伪微分方程α∈(0;本文考虑了作用于空间变量的阶。该方程自然地总结了已知的纯分数阶分形扩散方程。它出现在由运动物体引起的非平稳Riesz引力场的局部涡的数学建模中,其质量之间的相互作用用相应的Riesz势来表征。该方程的柯西问题的基本解是这些物体之间局部相互作用力概率的密度分布,它属于对称稳定随机过程的Polya分布。在一定条件下,对于局域场波动系数,建立了近似的极大值原理。这一原理对于证明柯西问题解在波动系数为非递减函数的时间区间上的统一性是非常重要的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
THE MAXIMUM PRINCIPLE FOR THE EQUATION OF LOCAL FLUCTUATIONS OF RIESZ GRAVITATIONAL FIELDS OF PURELY FRACTIONAL ORDER
The parabolic pseudodifferential equation with the Riesz fractional differentiation operator of α ∈ (0; 1) order, which acts on a spatial variable, is considered in the paper. This equation naturally summarizes the known equation of fractal diffusion of purely fractional order. It arises in the mathematical modeling of local vortices of nonstationary Riesz gravitational fields caused by moving objects, the interaction between the masses of which is characterized by the corresponding Riesz potential. The fundamental solution of the Cauchy problem for this equati- on is the density distribution of the probabilities of the force of local interaction between these objects, it belongs to the class of Polya distributions of symmetric stable random processes. Under certain conditions, for the coefficient of local field fluctuations, an analogue of the maximum principle was established for this equation. This principle is important in particular for substantiating the unity of the solution of the Cauchy problem on a time interval where the fluctuation coefficient is a non-decreasing function.
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