Sun, Zejun; Zheng, Guang-Hui Solving linear Bayesian inverse problems using a fractional total variation-Gaussian (FTG) prior and transport map. (English) Zbl 07800942 Comput. Stat. 38, No. 4, 1811-1849 (2023). MSC: 62-08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Li-Li; Ding, Ming-Hui; Zheng, Guang-Hui A Hadamard fractional total variation-Gaussian (HFTG) prior for Bayesian inverse problems. (English) Zbl 07725200 Inverse Probl. Imaging 17, No. 6, 1249-1276 (2023). MSC: 62F15 65C05 65N21 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Jiang, Yi; Liu, Jun; Wang, Xiang-Sheng A direct parallel-in-time quasi-boundary value method for inverse space-dependent source problems. (English) Zbl 1505.65254 J. Comput. Appl. Math. 423, Article ID 114958, 19 p. (2023). MSC: 65M32 65M30 65M12 65M15 65F35 65F05 65J20 65Y05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Xue, Xuemin; Xiong, Xiangtuan; Zhang, Yuanxiang Two fractional regularization methods for identifying the radiogenic source of the helium production-diffusion equation. (English) Zbl 1525.65090 AIMS Math. 6, No. 10, 11425-11448 (2021). MSC: 65M32 35K05 35R30 65J10 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Umbricht, Guillermo Federico Identification of the source for full parabolic equations. (English) Zbl 1486.35475 Math. Model. Anal. 26, No. 3, 339-357 (2021). MSC: 35R30 35R25 35K20 47A52 58J35 65T50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Liu, Songshu; Sun, Fuquan; Feng, Lixin Regularization of inverse source problem for fractional diffusion equation with Riemann-Liouville derivative. (English) Zbl 1476.65285 Comput. Appl. Math. 40, No. 4, Paper No. 112, 18 p. (2021). MSC: 65N21 65N20 × Cite Format Result Cite Review PDF Full Text: DOI
Coşkun, Arzu Erdem An inverse problem in estimating the time dependent source term and initial temperature simultaneously by the polynomial regression and conjugate gradient method. (English) Zbl 1499.35705 Filomat 34, No. 10, 3507-3516 (2020). MSC: 35R25 35R30 35K15 62J02 90C52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Amin, Mohammed Elmustafa; Xiong, Xiangtuan Source identification problems for radially symmetric and axis-symmetric heat conduction equations. (English) Zbl 1432.65137 Appl. Numer. Math. 138, 1-18 (2019). MSC: 65M32 35K20 35R30 80A23 × Cite Format Result Cite Review PDF Full Text: DOI
Qiu, Shufang; Wang, Zewen; Xie, Anlai Multivariate numerical derivative by solving an inverse heat source problem. (English) Zbl 07039163 Inverse Probl. Sci. Eng. 26, No. 8, 1178-1197 (2018). MSC: 65D25 65J22 × Cite Format Result Cite Review PDF Full Text: DOI
Yang, Fan; Ren, Yu-Peng; Li, Xiao-Xiao Landweber iteration regularization method for identifying unknown source on a columnar symmetric domain. (English) Zbl 1409.65066 Inverse Probl. Sci. Eng. 26, No. 8, 1109-1129 (2018). MSC: 65M32 35R30 35R25 35K20 80A23 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Yuan-Xiang; Yan, Liang The general a posteriori truncation method and its application to radiogenic source identification for the helium production-diffusion equation. (English) Zbl 1446.65099 Appl. Math. Modelling 43, 126-138 (2017). MSC: 65M32 65M30 35R25 35R30 35J05 80A23 × Cite Format Result Cite Review PDF Full Text: DOI
Tan, Yixuan; Zheng, Chengjian; Wen, John T.; Maniatty, Antoinette M. Inverse heat transfer analysis for design and control of a micro-heater array. (English) Zbl 1394.80013 Inverse Probl. Sci. Eng. 25, No. 9, 1259-1277 (2017). Reviewer: Aleksey Syromyasov (Saransk) MSC: 80A23 35Q79 65F22 93B52 80M10 65M60 × Cite Format Result Cite Review PDF Full Text: DOI
Zhao, Zhi-Xue; Banda, Mapundi K.; Guo, Bao-Zhu Simultaneous identification of diffusion coefficient, spacewise dependent source and initial value for one-dimensional heat equation. (English) Zbl 1368.93135 Math. Methods Appl. Sci. 40, No. 10, 3552-3565 (2017). MSC: 93B30 93C20 35K20 × Cite Format Result Cite Review PDF Full Text: DOI
Yang, Fan; Fu, Chu-Li; Li, Xiao-Xiao A mollification regularization method for identifying the time-dependent heat source problem. (English) Zbl 1380.65230 J. Eng. Math. 100, 67-80 (2016). MSC: 65M32 35R25 35R30 47A52 35K20 65M15 × Cite Format Result Cite Review PDF Full Text: DOI
Cheng, Wei Regularization and stability estimates for an inverse source problem of the radially symmetric parabolic equation. (English) Zbl 1516.35502 J. Inequal. Appl. 2015, Paper No. 136, 10 p. (2015). MSC: 35R30 35B45 35K20 65J20 65M30 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Erdem, Arzu A simultaneous approach to inverse source problem by Green’s function. (English) Zbl 1325.35277 Math. Methods Appl. Sci. 38, No. 7, 1393-1404 (2015). MSC: 35R30 35J08 35K20 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Zewen; Qiu, Shufang; Ruan, Zhousheng; Zhang, Wen A regularized optimization method for identifying the space-dependent source and the initial value simultaneously in a parabolic equation. (English) Zbl 1350.65107 Comput. Math. Appl. 67, No. 7, 1345-1357 (2014). MSC: 65M32 35R30 35K20 65M60 × Cite Format Result Cite Review PDF Full Text: DOI
Yang, Fan; Fu, Chu-Li; Li, Xiao-Xiao A quasi-boundary value regularization method for determining the heat source. (English) Zbl 1310.35243 Math. Methods Appl. Sci. 37, No. 18, 3026-3035 (2014). MSC: 35R25 35R30 65M30 × Cite Format Result Cite Review PDF Full Text: DOI
Erdem, A.; Lesnic, D.; Hasanov, A. Identification of a spacewise dependent heat source. (English) Zbl 1427.35355 Appl. Math. Modelling 37, No. 24, 10231-10244 (2013). MSC: 35R30 35K05 35K20 65M32 × Cite Format Result Cite Review PDF Full Text: DOI
Yang, Fan; Fu, Chu-Li The revised generalized Tikhonov regularization for the inverse time-dependent heat source problem. (English) Zbl 1304.47014 J. Appl. Math. Comput. 41, No. 1-2, 81-98 (2013). MSC: 47A52 35R25 65J20 65J22 × Cite Format Result Cite Review PDF Full Text: DOI
Dou, Fangfang Wavelet-Galerkin method for identifying an unknown source term in a heat equation. (English) Zbl 1264.65166 Math. Probl. Eng. 2012, Article ID 904183, 22 p. (2012). MSC: 65M70 35K15 35R30 × Cite Format Result Cite Review PDF Full Text: DOI
Li, Xiao-Xiao; Yang, Fan The truncation method for identifying the heat source dependent on a spatial variable. (English) Zbl 1231.80039 Comput. Math. Appl. 62, No. 6, 2497-2505 (2011). MSC: 80A22 65M32 35K05 35K20 65R30 × Cite Format Result Cite Review PDF Full Text: DOI
Yang, Fan; Fu, Chu-Li Two regularization methods to identify time-dependent heat source through an internal measurement of temperature. (English) Zbl 1217.65183 Math. Comput. Modelling 53, No. 5-6, 793-804 (2011). MSC: 65M32 35R30 35K20 × Cite Format Result Cite Review PDF Full Text: DOI
Yan, Liang; Yang, Fenglian; Fu, Chuli A new numerical method for the inverse source problem from a Bayesian perspective. (English) Zbl 1217.80154 Int. J. Numer. Methods Eng. 85, No. 11, 1460-1474 (2011). MSC: 80M25 80A23 80A20 × Cite Format Result Cite Review PDF Full Text: DOI
Mierzwiczak, Magdalena; Kołodziej, Jan Adam Application of the method of fundamental solutions and radial basis functions for inverse transient heat source problem. (English) Zbl 1219.65101 Comput. Phys. Commun. 181, No. 12, 2035-2043 (2010). MSC: 65M32 35K05 35R30 65M80 65M06 × Cite Format Result Cite Review PDF Full Text: DOI
Yang, Fan; Fu, Chu-Li A simplified Tikhonov regularization method for determining the heat source. (English) Zbl 1201.65177 Appl. Math. Modelling 34, No. 11, 3286-3299 (2010). MSC: 65M32 80M25 35R30 × Cite Format Result Cite Review PDF Full Text: DOI
Yang, Fan; Fu, Chu-Li The method of simplified Tikhonov regularization for dealing with the inverse time-dependent heat source problem. (English) Zbl 1201.65176 Comput. Math. Appl. 60, No. 5, 1228-1236 (2010). MSC: 65M32 35K10 80A22 80M25 × Cite Format Result Cite Review PDF Full Text: DOI