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Inverse Problems in Science and Engineering Volume 17, 2009 - Issue 7
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Original Articles

Identifying an unknown source term in a heat equation

Fang-Fang DouSchool of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P.R.China
,
Chu-Li FuSchool of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P.R.China
&
Fan YangSchool of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P.R.China;Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, P.R. China
Pages 901-913 | Received 01 Jun 2008, Accepted 18 Oct 2008, Published online: 16 Sep 2009

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Zhengqiang Zhang & Yuan-Xiang Zhang. (2022) A fast iterative method for identifying the radiogenic source for the helium production-diffusion equation. Applied Mathematics in Science and Engineering 30:1, pages 521-540.
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Nguyen Van Duc, Nguyen Van Thang, Luong Duy Nhat Minh & Nguyen Trung Thành. (2022) Identifying an unknown source term of a parabolic equation in Banach spaces. Applicable Analysis 101:6, pages 2066-2084.
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Nguyen Van Duc, Luong Duy Nhat Minh & Nguyen Trung Thanh. (2021) Identifying an unknown source term in a heat equation with time-dependent coefficients. Inverse Problems in Science and Engineering 29:5, pages 609-635.
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Fan Yang, Yu-Peng Ren & Xiao-Xiao Li. (2018) Landweber iteration regularization method for identifying unknown source on a columnar symmetric domain. Inverse Problems in Science and Engineering 26:8, pages 1109-1129.
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Zehong Meng & Zhenyu Zhao. (2017) Hermite spectral method for solving inverse heat source problems in multiple dimensions. Inverse Problems in Science and Engineering 25:9, pages 1243-1258.
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Yi Jiang, Jun Liu & Xiang-Sheng Wang. (2023) A direct parallel-in-time quasi-boundary value method for inverse space-dependent source problems. Journal of Computational and Applied Mathematics 423, pages 114958.
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Fermín S. V. Bazán, Luciano Bedin, Koung Hee Leem, Jun Liu & George Pelekanos. (2023) Fast matrix exponential-based quasi-boundary value methods for inverse space-dependent source problems. Networks and Heterogeneous Media 18:2, pages 601-621.
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Nguyen Van Duc, Nguyen Van Thang & Nguyen Trung Thành. (2023) The quasi-reversibility method for an inverse source problem for time-space fractional parabolic equations. Journal of Differential Equations 344, pages 102-130.
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J J Cadena-Morales, C A López-Castro & J M Alba-Maldonado. (2021) Applications of differential equations to model the physical phenomenon of heat transfer with an internal energy source. Journal of Physics: Conference Series 2102:1, pages 012018.
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Nguyen Van Thang, Nguyen Van Duc, Luong Duy Nhat Minh & Nguyen Trung Thành. (2021) Identifying an unknown source term in a time-space fractional parabolic equation. Applied Numerical Mathematics 166, pages 313-332.
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Shuli Chen, Zewen Wang & Guolin Chen. (2021) Cauchy problem of non-homogenous stochastic heat equation and application to inverse random source problem. Inverse Problems & Imaging 15:4, pages 619.
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J. Damirchi, R. Pourgholi, T. R. Shamami, H. Zeidabadi & A. Janmohammadi. (2021) Identification of a Time Dependent Source Function in a Parabolic Inverse Problem Via Finite Element Approach. Indian Journal of Pure and Applied Mathematics 51:4, pages 1587-1602.
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Zewen Wang, Shuli Chen, Shufang Qiu & Bin Wu. (2020) A non-iterative method for recovering the space-dependent source and the initial value simultaneously in a parabolic equation. Journal of Inverse and Ill-posed Problems 28:4, pages 499-516.
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Nguyen Minh Dien, Dinh Nguyen Duy Hai, Tran Quoc Viet & Dang Duc Trong. (2020) On Tikhonov’s method and optimal error bound for inverse source problem for a time-fractional diffusion equation. Computers & Mathematics with Applications 80:1, pages 61-81.
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F. Kanca & I. Baglan. (2020) Solution of the Boundary-Value Problem of Heat Conduction with Periodic Boundary Conditions. Ukrainian Mathematical Journal 72:2, pages 232-245.
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Xiangtuan Xiong & Xuemin Xue. (2019) A fractional Tikhonov regularization method for identifying a space-dependent source in the time-fractional diffusion equation. Applied Mathematics and Computation 349, pages 292-303.
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Coskun Guler & Volkan Oban. (2017) On the Inverse Problem of Dupire’s Equation with Nonlocal Boundary and Integral Conditions. Journal of Mathematical Finance 07:04, pages 934-940.
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Fan Yang, Chu-Li Fu & Xiao-Xiao Li. (2016) A mollification regularization method for identifying the time-dependent heat source problem. Journal of Engineering Mathematics 100:1, pages 67-80.
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Jun-Gang Wang & Ting Wei. (2015) Quasi-reversibility method to identify a space-dependent source for the time-fractional diffusion equation. Applied Mathematical Modelling 39:20, pages 6139-6149.
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Fan Yang, Chu-Li Fu & Xiao-Xiao Li. (2014) A quasi-boundary value regularization method for determining the heat source. Mathematical Methods in the Applied Sciences 37:18, pages 3026-3035.
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Guanglu Zhou & Boying Wu. (2014) Identifying a time-dependent heat source with nonlocal boundary and overdetermination conditions by the variational iteration method. International Journal of Numerical Methods for Heat & Fluid Flow 24:7, pages 1545-1552.
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Zewen Wang, Shufang Qiu, Zhousheng Ruan & Wen Zhang. (2014) A regularized optimization method for identifying the space-dependent source and the initial value simultaneously in a parabolic equation. Computers & Mathematics with Applications 67:7, pages 1345-1357.
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Xiangtuan Xiong & Junxia Wang. (2012) A Tikhonov-type method for solving a multidimensional inverse heat source problem in an unbounded domain. Journal of Computational and Applied Mathematics 236:7, pages 1766-1774.
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M.I. Ismailov, F. Kanca & D. Lesnic. (2011) Determination of a time-dependent heat source under nonlocal boundary and integral overdetermination conditions. Applied Mathematics and Computation 218:8, pages 4138-4146.
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Fan Yang. (2011) The truncation method for identifying an unknown source in the Poisson equation. Applied Mathematics and Computation 217:22, pages 9334-9339.
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Ailin Qian & Yongxin Gui. (2010) Determining an Unknown Source in the Heat Equation by a Mollification Regularization Method. Determining an Unknown Source in the Heat Equation by a Mollification Regularization Method.

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