JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (6): 64-73.doi: 10.6040/j.issn.1671-9352.0.2020.582

Previous Articles    

Identification of source term for fractional diffusion-wave equation with Neumann boundary conditions

QI Bin, CHENG Hao*   

  1. School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China
  • Published:2021-06-03

PDF (PC)

197

Abstract: The source term identification of the time-fractional diffusion-wave equation with Neumann boundary conditions is studied. An improved iterative regularization method is constructed to calculate the regularization solution of the source term. The error estimates between the regularization solution and the exact solution are given under the prior and the posterior regularization parameter choice rules. Numerical examples verify the effectiveness of the iterative regularization method.

Key words: fractional diffusion-wave equation, source term identification, iterative regularization, error estimate

CLC Number: 

  • O241.82
[1] SUN Hongguang, CHEN Wen, LI Changping, et al. Fractional differential models for anomalous diffusion[J]. Physica A, 2010, 389(14):2719-2724.
[2] LIU F W, MEERSCHAERT M M, MCGOUGH R J, et al. Numerical methods for solving the multi-term time-fractional wave-diffusion equation[J]. Fractional Calculus and Applied Analysis, 2013, 16(1):9-25.
[3] MAINARDI F. The fundamental solutions for the fractional diffusion-wave equation[J]. Applied Mathematics Letters, 1996, 9(6):23-28.
[4] DU Rui, CAO Wanrong, SUN Zhizhong. A compact difference scheme for the fractional diffusion-wave equation[J]. Applied Mathematical Modelling, 2010, 34(10):2998-3007.
[5] HU G H, LIU Y K, YAMAMOTO M. Inverse moving source problem for fractional diffusion(-wave)equations: determination of orbits[J]. Inverse Problems and Related Topics, 2020, 310:81-100.
[6] SAKAMOTO K, YAMAMOTO M. Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems[J]. Journal of Mathematical Analysis and Applications, 2011, 382(1):426-447.
[7] JIANG Suzhen, LIAO Kaifang, WEI Ting. Inversion of the initial value for a time-fractional diffusion-wave equation by boundary data[J]. Computational Methods in Applied Mathematics, 2020, 20(1):109-120.
[8] YANG Fan, PU Qu, LI Xiaoxiao, et al. The truncation regularization method for identifying the initial value on non-homogeneous time-fractional diffusion-wave equations[J]. Mathematics, 2019, 7(11):1007.
[9] LI Gongsheng, ZHANG Dali, JIA Xianzheng, et al. Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation[J]. Inverse Problems, 2013, 29(6):65014-65049.
[10] GONG Xuhong, WEI Ting. Reconstruction of a time-dependent source term in a time-fractional diffusion-wave equation[J]. Inverse Problems in Science and Engineering, 2019, 27(11):1577-1594.
[11] YAN Xiongbin, WEi Ting. Determine a space-dependent source term in a time fractional diffusion-wave equation[J]. Acta Applicandae Mathematicae, 2020, 165(1):163-181.
[12] YANG Fan, WANG Ni, LI Xiaoxiao. Landweber iterative method for an inverse source problem of time-fractional diffusion-wave equation on spherically symmetric domain[J]. Journal of Applied Analysis and Computation, 2020, 10(2):514-529.
[13] LONG L D, LUC N H, ZHOU Y, et al. Identification of source term for the time-fractional diffusion-wave equation by fractional Tikhonov method[J]. Mathematics, 2019, 7(10):934.
[14] WANG Jungang, Ran Yuhong. An iterative method for an inverse source problem of time-fractional diffusion equation[J]. Inverse Problems in Scienceand Engineering, 2018, 26(10):1509-1521.
[15] PODLUBNY I. Fractional differential equations[M]. San Diego: Academic Press, 1999.
[16] DENG Youjun, LIU Zhenhai. Iteration methods on sideways parabolic equations[J]. Inverse Problems, 2009, 25(9):095004.
[17] 李晓婷.时间分数阶扩散波方程的反源项问题[D]. 兰州:兰州大学,2017. LI Xiaoting. Inverse source problem for a time fractional diffusion-wave equation[D]. Lanzhou: Lanzhou University, 2017.
[1] YANG Cai-jie, SUN Tong-jun. Crank-Nicolson finite difference method for parabolic optimal control problem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(6): 115-121.
[2] ZHENG Rui-rui, SUN Tong-jun. A priori error estimates of finite element methods for an optimal control problem governed by a one-prey and one-predator model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(1): 23-32.
[3] SHI Yan-hua1, SHI Dong-yang2*. The quasi-Wilson nonconforming finite element approximation to  pseudo-hyperbolic equations [J]. J4, 2013, 48(4): 77-84.
[4] WU Zhi-qin1, SHI Dong-wei2. Convergence analysis for nonlinear integro-differential equations with a weakly singular kernel [J]. J4, 2012, 47(8): 60-63.
[5] LI Na, GAO Fu-zheng*, ZHANG Tian-de. An expanded mixed covolume method for Sobolev equations [J]. J4, 2012, 47(6): 34-39.
[6] YU Jin-biao1,2, XI Kai-hua3*, DAI Tao2, LU Tong-chao3, YANG Yao-zhong2, . Convergence of the finite element method for two-phase multi-component flow in porous media [J]. J4, 2012, 47(2): 19-25.
[7] ZHOU Jia-quan, SUN Ying-de， ZHANG Yong-sheng. A nonconforming characteristic finite element method for Burgers equations [J]. J4, 2012, 47(12): 103-108.
[8] QIAO Bao-min, LIANG Hong-liang. Super-convergence analysis of Adini′s finite element for a kind of nonlinear generalized nerve conductive equations [J]. J4, 2011, 46(8): 42-46.
[9] ZHENG Rui-rui, SUN Tong-jun. An upwind-mixed method for the linear Sobolev equation [J]. J4, 2011, 46(4): 23-28.
[10] MA Ning. Orthogonal collocation method for miscible displacement with dispersion [J]. J4, 2011, 46(2): 78-81.
[11] LU Yao1, LI De-sheng2, YANG Yang1. The Fourier spectral approximation for nonlinear SchrÖdinger equation [J]. J4, 2011, 46(1): 119-126.
[12] LI Zhi-tao. The finite difference method of  miscible displacement problems in deformable porous media [J]. J4, 2010, 45(6): 50-55.
[13] . The finite element method for  controlledrelease and spread of solute coupling with fluid velocity in a porous medium [J]. J4, 2009, 44(2): 33-38.
[14] . Galerkin methods for twophase multicomponents flow in porous media [J]. J4, 2009, 44(12): 6-13.
[15] LI Zhi-tao . Characteristic mixed finiteelement method of dynamic grid driven by miscible fluid in porous media [J]. J4, 2007, 42(4): 19-23 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd