Uniqueness and Existence for Inverse Problem of Determining an Order of Time-Fractional Derivative of Subdiffusion Equation

被引：13

作者：

Ashurov, R. R. ^{[1
]}

Fayziev, Yu E. ^{[2
]}

机构：

[1] Acad Sci Uzbek, Inst Math, Tashkent 100170, Uzbekistan

[2] Natl Univ Uzbekistan, Tashkent 700174, Uzbekistan

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2021年 / 42卷 / 03期

关键词：

nonhomogeneous subdiffusion equation; Riemann-Liouville derivatives; inverse and initial-boundary value problem; determination of the fractional derivative's order; Fourier method; OPERATOR;

D O I：

10.1134/S1995080221030069

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An inverse problem for determining the order of time-fractional derivative in a nonhomogeneous subdiffusion equation with an arbitrary elliptic differential operator with constant coefficients in N-dimensional torus is considered. Using the classical Fourier method it is proved, that the value of the solution at a fixed time instant as the observation data recovers uniquely the order of fractional derivative. Generalization to an arbitrary N-dimensional domain and to elliptic operators with variable coefficients is considered.

引用

页码：508 / 516

页数：9

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