On existence and regularity of a terminal value problem for the time fractional diffusion equation

被引：19

作者：

Nguyen Huy Tuan ^{[1
]}

Tran Bao Ngoc ^{[2
]}

Zhou, Yong ^{[3
,4
]}

O'Regan, Donal ^{[5
]}

机构：

[1] Ton Duc Thang Univ, Fac Math & Stat, Appl Anal Res Grp, Ho Chi Minh City, Vietnam

[2] Duy Tan Univ, Inst Res & Dev, Da Nang 550000, Vietnam

[3] Macau Univ Sci & Technol, Fac Informat Technol, Macau, Peoples R China

[4] Xiangtan Univ, Fac Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

[5] Natl Univ Ireland, Sch Math Stat & Appl Math, Galway, Ireland

来源：

INVERSE PROBLEMS | 2020年 / 36卷 / 05期

关键词：

existence and regularity; final value problem; time fractional derivative; uniqueness; BACKWARD PROBLEM; PARABOLIC PROBLEM; INVERSE PROBLEM; WELL-POSEDNESS; WAVE-EQUATIONS; WEAK SOLUTIONS; UNIQUENESS;

D O I：

10.1088/1361-6420/ab730d

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider a final value problem for a diffusion equation with time-space fractional differentiation on a bounded domain D of Rk<i, k >= 1, which includes the fractional power L beta<i, 0 < beta <= 1, of a symmetric uniformly elliptic operator LL2(D). A representation of solutions is given by using the Laplace transform and the spectrum of L beta<i. We establish some existence and regularity results for our problem in both the linear and nonlinear case.

引用

页数：41

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