Lipschitz Stability in Inverse Source and Inverse Coefficient Problems for a First- and Half-order Time-fractional Diffusion Equation

Atsushi Kawamoto; Manabu Machida

doi:10.1137/18m1235776

Lipschitz Stability in Inverse Source and Inverse Coefficient Problems for a First- and Half-order Time-fractional Diffusion Equation

SIAM Journal on Mathematical Analysis ◽

10.1137/18m1235776 ◽

2020 ◽

Vol 52 (1) ◽

pp. 967-1005

Author(s):

Atsushi Kawamoto ◽

Manabu Machida

Keyword(s):

Diffusion Equation ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Lipschitz Stability ◽

Inverse Coefficient Problems ◽

Coefficient Problems ◽

Time Fractional Diffusion Equation ◽

Inverse Coefficient

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Uniqueness for an inverse coefficient problem for a one-dimensional time-fractional diffusion equation with non-zero boundary conditions

Applicable Analysis ◽

10.1080/00036811.2021.1965583 ◽

2021 ◽

pp. 1-15

Author(s):

William Rundell ◽

Masahiro Yamamoto

Keyword(s):

Diffusion Equation ◽

Boundary Conditions ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Coefficient Problem ◽

Inverse Coefficient Problem ◽

One Dimensional ◽

Time Fractional Diffusion Equation ◽

Inverse Coefficient

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Blow-up solutions of a time-fractional diffusion equation with variable exponents

Tbilisi Mathematical Journal ◽

10.32513/tbilisi/1578020574 ◽

2019 ◽

Vol 12 (4) ◽

pp. 149-157

Author(s):

J. Manimaran ◽

L. Shangerganesh

Keyword(s):

Diffusion Equation ◽

Blow Up ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Variable Exponents ◽

Time Fractional Diffusion Equation

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On inverse source problem for time fractional diffusion equation on simple metric graph

Uzbek Mathematical Journal ◽

10.29229/uzmj.2020-2-10 ◽

2020 ◽

Vol 2020 (2) ◽

pp. 99-108

Author(s):

J.R. Khujakulov

Keyword(s):

Diffusion Equation ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Inverse Source Problem ◽

Metric Graph ◽

Time Fractional Diffusion Equation

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An Error Estimate of a Numerical Approximation to a Hidden-Memory Variable-Order Space-Time Fractional Diffusion Equation

SIAM Journal on Numerical Analysis ◽

10.1137/20m132420x ◽

2020 ◽

Vol 58 (5) ◽

pp. 2492-2514

Author(s):

Xiangcheng Zheng ◽

Hong Wang

Keyword(s):

Diffusion Equation ◽

Error Estimate ◽

Numerical Approximation ◽

Fractional Diffusion ◽

Space Time ◽

Fractional Diffusion Equation ◽

Variable Order ◽

Time Fractional Diffusion Equation

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Numerical investigation of the two-dimensional space-time fractional diffusion equation in porous media

Mathematical Sciences ◽

10.1007/s40096-020-00364-3 ◽

2021 ◽

Author(s):

B. Farnam ◽

Y. Esmaeelzade Aghdam ◽

O. Nikan

Keyword(s):

Porous Media ◽

Diffusion Equation ◽

Numerical Investigation ◽

Dimensional Space ◽

Fractional Diffusion ◽

Space Time ◽

Fractional Diffusion Equation ◽

Two Dimensional ◽

Dimensional Space Time ◽

Time Fractional Diffusion Equation

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Homotopy perturbation method to time-fractional diffusion equation with a moving boundary condition

Applied Mathematics and Computation ◽

10.1016/j.amc.2008.12.023 ◽

2009 ◽

Vol 208 (2) ◽

pp. 434-439 ◽

Cited By ~ 33

Author(s):

Xicheng Li ◽

Mingyu Xu ◽

Xiaoyun Jiang

Keyword(s):

Boundary Condition ◽

Diffusion Equation ◽

Perturbation Method ◽

Homotopy Perturbation Method ◽

Moving Boundary ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Homotopy Perturbation ◽

Moving Boundary Condition ◽

Time Fractional Diffusion Equation

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Reconstruction of the temporal component in the source term of a (time-fractional) diffusion equation

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8121/aa763a ◽

2017 ◽

Vol 50 (30) ◽

pp. 305203 ◽

Cited By ~ 7

Author(s):

Yikan Liu ◽

Zhidong Zhang

Keyword(s):

Diffusion Equation ◽

Source Term ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Time Fractional Diffusion Equation

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Tikhonov regularization method for identifying the space-dependent source for time-fractional diffusion equation on a columnar symmetric domain

Advances in Difference Equations ◽

10.1186/s13662-020-2542-1 ◽

2020 ◽

Vol 2020 (1) ◽

Cited By ~ 8

Author(s):

Fan Yang ◽

Pan Zhang ◽

Xiao-Xiao Li ◽

Xin-Yi Ma

Keyword(s):

Diffusion Equation ◽

Tikhonov Regularization ◽

Regularization Method ◽

Symmetric Domain ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Tikhonov Regularization Method ◽

Time Fractional Diffusion Equation

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A Numerical Method for Solving the Inverse Source Problem of the Space-Time Fractional Diffusion Equation

Advances in Applied Mathematics ◽

10.12677/aam.2021.104108 ◽

2021 ◽

Vol 10 (04) ◽

pp. 996-1002

Author(s):

柔姿段

Keyword(s):

Diffusion Equation ◽

Numerical Method ◽

Fractional Diffusion ◽

Space Time ◽

Fractional Diffusion Equation ◽

Inverse Source Problem ◽

Time Fractional Diffusion Equation

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A second-order scheme for a time-fractional diffusion equation

Applied Mathematics Letters ◽

10.1016/j.aml.2018.10.016 ◽

2019 ◽

Vol 90 ◽

pp. 79-85 ◽

Cited By ~ 3

Author(s):

Zhongdi Cen ◽

Jian Huang ◽

Anbo Le ◽

Aimin Xu

Keyword(s):

Diffusion Equation ◽

Fractional Diffusion ◽

Second Order ◽

Fractional Diffusion Equation ◽

Order Scheme ◽

Time Fractional Diffusion Equation

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