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Articles

Inverse source problem in a one-dimensional evolution linear transport equation with spatially varying coefficients: application to surface water pollution

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Pages 1007-1031 | Received 11 Sep 2011, Accepted 07 Jan 2013, Published online: 18 Feb 2013

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Adel Hamdi & Antoine Tonnoir. (2021) Dispersion–current adjoint functions for monitoring accidental sources in 3D transport equations. Inverse Problems in Science and Engineering 29:10, pages 1445-1476.
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M. Kulbay, B. Mukanova & C. Sebu. (2017) Identification of separable sources for advection-diffusion equations with variable diffusion coefficient from boundary measured data. Inverse Problems in Science and Engineering 25:2, pages 279-308.
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Xiaomao Deng, Zi-Ju Liao & Xiao-Chuan Cai. (2022) An efficient two-level overlapping domain decomposition method for recovering unsteady sources of 3D parabolic problems. Computers & Mathematics with Applications 111, pages 98-108.
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Guangpeng Zhang, Tao Ding, Guangjie Zhan, Xinyi Du & Danjia Yan. (2021) Early Warning and Source Identification System Design for Chemical Spill Incidents of Jinhua River. IOP Conference Series: Earth and Environmental Science 787:1, pages 012185.
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Anis Bel Hadj Hassin, Nejla T. Hariga & Faten Khayat. (2020) Data completion problem for the advection‐diffusion equation with aquifer point sources. Mathematical Methods in the Applied Sciences 44:2, pages 1651-1663.
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V.V. Vesselinov, M.K. Mudunuru, S. Karra, D. O'Malley & B.S. Alexandrov. (2019) Unsupervised machine learning based on non-negative tensor factorization for analyzing reactive-mixing. Journal of Computational Physics 395, pages 85-104.
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Jiping Jiang, Yasong Chen & Baoyu Wang. (2019) Pollution Source Identification for River Chemical Spills by Modular-Bayesian Approach: A Retrospective Study on the ‘Landmark’ Spill Incident in China. Hydrology 6:3, pages 74.
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Velimir V. Vesselinov, Boian S. Alexandrov & Daniel O'Malley. (2019) Nonnegative tensor factorization for contaminant source identification. Journal of Contaminant Hydrology 220, pages 66-97.
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Valentin G. Stanev, Filip L. Iliev, Scott Hansen, Velimir V. Vesselinov & Boian S. Alexandrov. (2018) Identification of release sources in advection–diffusion system by machine learning combined with Green’s function inverse method. Applied Mathematical Modelling 60, pages 64-76.
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Velimir V. Vesselinov, Boian S. Alexandrov & Daniel O’Malley. (2018) Contaminant source identification using semi-supervised machine learning. Journal of Contaminant Hydrology 212, pages 134-142.
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Adel Hamdi & Imed Mahfoudhi. (2016) Inverse source problem based on two dimensionless dispersion-current functions in 2D evolution transport equations. Journal of Inverse and Ill-posed Problems 24:6, pages 663-685.
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Wei Guozhen, Chi Zhang, Yu Li, Liu Haixing & Huicheng Zhou. (2016) Source identification of sudden contamination based on the parameter uncertainty analysis. Journal of Hydroinformatics 18:6, pages 919-927.
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Adel Hamdi, Imed Mahfoudhi & Ahmed Rejaiba. (2015) Identification of time active limit with lower and upper bounds of total amount loaded by unknown sources in 2D transport equations. Journal of Engineering Mathematics 97:1, pages 101-117.
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Haidong Yang, Dongguo Shao, Biyu Liu, Jianhua Huang & Xianbao Ye. (2015) Multi-point source identification of sudden water pollution accidents in surface waters based on differential evolution and Metropolis–Hastings–Markov Chain Monte Carlo. Stochastic Environmental Research and Risk Assessment 30:2, pages 507-522.
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V.T. Borukhov & G.M. Zayats. (2015) Identification of a time-dependent source term in nonlinear hyperbolic or parabolic heat equation. International Journal of Heat and Mass Transfer 91, pages 1106-1113.
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I. G. Stratis & A. N. Yannacopoulos. (2015) Some remarks on a class of inverse problems related to the parabolic approximation to the Maxwell equations: a controllability approach. Mathematical Methods in the Applied Sciences 38:17, pages 3866-3878.
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