On Time-Fractional Diffusion Equations with Space-Dependent Variable Order

被引：43

作者：

Kian, Yavar ^{[1
]}

Soccorsi, Eric ^{[1
]}

Yamamoto, Masahiro ^{[2
,3
]}

机构：

[1] Aix Marseille Univ, Univ Toulon, CNRS, CPT, Marseille, France

[2] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, 3-8-1 Komaba, Tokyo 1538914, Japan

[3] RUDN Univ, Peoples Friendship Univ Russia, 6 Miklukho Maklaya St, Moscow 117198, Russia

来源：

ANNALES HENRI POINCARE | 2018年 / 19卷 / 12期

基金：

日本学术振兴会;

关键词：

BOUNDARY-VALUE-PROBLEMS; ANOMALOUS DIFFUSION; UNIQUENESS; CALCULUS;

D O I：

10.1007/s00023-018-0734-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper deals with mathematical problems related to space-dependent anomalous diffusion processes. Namely, we investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We establish that variable-order time-fractional Cauchy problems admit a unique weak solution and prove that the space-dependent variable-order coefficient is uniquely determined by the knowledge of a suitable time sequence of partial initial-boundary maps.

引用

页码：3855 / 3881

页数：27

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