EXACT ASYMPTOTIC FORMULAS FOR THE HEAT KERNELS OF SPACE AND TIME-FRACTIONAL EQUATIONS

被引：2
作者：
Deng, Chang-Song [1 ]
Schilling, Rene L. [2 ]
机构：
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China
[2] Tech Univ Dresden, Fak Math, Inst Math Stochast, D-01062 Dresden, Germany
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2019年 / 22卷 / 04期
基金：
中国国家自然科学基金;
关键词：
heat kernel; asymptotic formula; space-fractional equation; time-fractional equation; subordinator; inverse subordinator; ANOMALOUS DIFFUSION; BROWNIAN-MOTION; RANDOM-WALKS;
D O I：
10.1515/fca-2019-0052
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper aims to study the asymptotic behaviour of the fundamental solutions (heat kernels) of non-local (partial and pseudo differential) equations with fractional operators in time and space. In particular, we obtain exact asymptotic formulas for the heat kernels of time-changed Brownian motions and Cauchy processes. As an application, we obtain exact asymptotic formulas for the fundamental solutions to the n-dimensional fractional heat equations in both time and space partial derivative(beta)/partial derivative t(beta) u(t, x) = -(-Delta(x))(gamma)u(t, x), beta, gamma is an element of(0, 1).
引用
收藏
页码：968 / 989
页数：22
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