Inverse moving source problem for time-fractional evolution equations: determination of profiles

被引：10

作者：

Liu, Yikan ^{[1
]}

Hu, Guanghui ^{[2
,3
]}

Yamamoto, Masahiro ^{[4
,5
,6
,7
]}

机构：

[1] Hokkaido Univ, Res Ctr Math Social Creat, Res Inst Elect Sci, N12W7 Kita Ward, Sapporo, Hokkaido 0600812, Japan

[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

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

[5] Acad Romanian Scientists, Ilfov 3, Bucharest, Romania

[6] Acead Peloritana Pericolanti, Palazzo Univ,Piazza S Pugliatti 1, I-98122 Messina, Italy

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

来源：

INVERSE PROBLEMS | 2021年 / 37卷 / 08期

基金：

中国国家自然科学基金; 日本学术振兴会;

关键词：

inverse moving source problem; time-fractional evolution equation; vanishing property; uniqueness; DIFFUSION EQUATION; DISPERSION; UNIQUENESS; STABILITY;

D O I：

10.1088/1361-6420/ac0c20

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article is concerned with two inverse problems on determining moving source profile functions in evolution equations with a derivative order alpha is an element of (0, 2] in time. In the first problem, the sources are supposed to move along known straight lines, and we suitably choose partial interior observation data in finite time. Reducing the problems to the determination of initial values, we prove the unique determination of one and two moving source profiles for 0 < alpha <= 1 and 1 < alpha <= 2, respectively. In the second problem, the orbits of moving sources are assumed to be known, and we consider the full lateral Cauchy data. At the cost of infinite observation time, we prove the unique determination of one moving source profile by constructing test functions.

引用

页数：24

共 36 条

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