带反射边区间上周期初值的反常扩散
Anomalous Diffusion with Periodical Initial Conditions on Interval with Reflecting Edges
摘要：
Uchaikin提出了空间反常扩散的数学模型。该模型起源于对具有可变结构的复杂系统（玻璃、液晶、生物聚合物、蛋白质等）中的过程的研究。在该模型中，粒子的坐标具有稳定分布（非正态分布）。结果，其分布函数的密度满足扩散方程的模拟，其中坐标的二阶导数被偏导数代替。本文研究了具有反射边的区间上周期初始条件下的反常扩散问题。例如，在技术力学中，这个问题对于分析直流发动机中的燃料混合也是重要的。作为匿名戒酒会。Borovkov建议开发特殊的概率方法来分析这种扩散。
英文摘要：
Uchaikin suggested a mathematical model of an anomalous diffusion in a space was suggested. This model origins in an investigation of processes in complex systems with variable structure: glasses, liquid crystals, biopolymers, proteins and etc. In this model a coordinate of a particle has stable distribution (not normal one). As a result a density of its distribution function satisfies an analog of diffusion equation in which second derivative by coordinate is replaced by partial derivative. In this paper the anomalous diffusion with periodic initial conditions on an interval with reflecting edges is considered. Such problem is important for example in technical mechanics for an analysis of fuel mixing in straight flow engine too. As A.A. Borovkov suggested special probability methods are developed to analyze such a diffusion.
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