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Original Articles

A modified Tikhonov regularization method for a backward heat equation

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Pages 1175-1182 | Received 06 Sep 2010, Accepted 09 Jul 2011, Published online: 11 Aug 2011

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Articles from other publishers (17)

Yi Jiang & Jun Liu. (2023) Fast parallel-in-time quasi-boundary value methods for backward heat conduction problems. Applied Numerical Mathematics 184, pages 325-339.
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V. I. Vasil’ev, A. M. Kardashevsky & V. V. Popov. (2023) Iterative Solution of a Retrospective Inverse Heat Conduction Problem with Inhomogeneous Dirichlet Boundary Conditions. Journal of Applied and Industrial Mathematics 16:4, pages 841-852.
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Guillermo Federico Umbricht. (2021) IDENTIFICATION OF THE SOURCE FOR FULL PARABOLIC EQUATIONS. Mathematical Modelling and Analysis 26:3, pages 339-357.
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Dmitry Lukyanenko, Tatyana Yeleskina, Igor Prigorniy, Temur Isaev, Andrey Borzunov & Maxim Shishlenin. (2021) Inverse Problem of Recovering the Initial Condition for a Nonlinear Equation of the Reaction–Diffusion–Advection Type by Data Given on the Position of a Reaction Front with a Time Delay. Mathematics 9:4, pages 342.
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Dmitry V. Lukyanenko, Igor V. Prigorniy & Maxim A. Shishlenin. (2020) Some features of solving an inverse backward problem for a generalized Burgers’ equation. Journal of Inverse and Ill-posed Problems 28:5, pages 641-649.
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Leif Bergerhoff, Marcelo Cárdenas, Joachim Weickert & Martin Welk. (2020) Stable Backward Diffusion Models that Minimise Convex Energies. Journal of Mathematical Imaging and Vision 62:6-7, pages 941-960.
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Jun Liu & Mingqing Xiao. (2019) Quasi-boundary value methods for regularizing the backward parabolic equation under the optimal control framework. Inverse Problems 35:12, pages 124003.
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V.I. Vasil’ev & M. Kardashevsky. (2019) Numerical identification of the initial condition for parabolic equation. Journal of Physics: Conference Series 1392:1, pages 012089.
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Fan Yang, Ya-Ru Sun, Xiao-Xiao Li & Cheng-Ye Ma. (2018) The truncation regularization method for identifying the initial value of heat equation on a spherical symmetric domain. Boundary Value Problems 2018:1.
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Pol del Aguila Pla & Joakim Jalden. (2018) Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity—Part I: Modeling and Inverse Problems. IEEE Transactions on Signal Processing 66:20, pages 5407-5421.
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V. I. Vasil’ev & A. M. Kardashevskii. (2018) Numerical Solution of the Retrospective Inverse Problem of Heat Conduction with the Help of the Poisson Integral. Journal of Applied and Industrial Mathematics 12:3, pages 577-586.
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ChunPing Ren, NengJian Wang & ChunSheng Liu. (2017) Identification of Random Dynamic Force Using an Improved Maximum Entropy Regularization Combined with a Novel Conjugate Gradient. Mathematical Problems in Engineering 2017, pages 1-14.
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V. I. Vasil’ev & A. M. Kardashevsky. 2017. Numerical Analysis and Its Applications. Numerical Analysis and Its Applications 698 705 .
V I Vasil'ev, A M Kardashevsky & PV Sivtsev. (2016) Computational experiment on the numerical solution of some inverse problems of mathematical physics. IOP Conference Series: Materials Science and Engineering 158, pages 012093.
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Elyas Shivanian & Hamid Reza Khodabandehlo. (2016) Application of meshless local radial point interpolation (MLRPI) on a one-dimensional inverse heat conduction problem. Ain Shams Engineering Journal 7:3, pages 993-1000.
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Fan YANG, Chuli FU & Xiaoxiao LI. (2015) A modified tikhonov regularization method for the cauchy problem of laplace equation. Acta Mathematica Scientia 35:6, pages 1339-1348.
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Fan YANG, Chuli FU & Xiaoxiao LI. (2014) Identifying an unknown source in space-fractional diffusion equation. Acta Mathematica Scientia 34:4, pages 1012-1024.
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