Liu, Chein-Shan; Qiu, Lin Solving the 2D and 3D nonlinear inverse source problems of elliptic type partial differential equations by a homogenization function method. (English) Zbl 07776963 Numer. Methods Partial Differ. Equations 39, No. 2, 1287-1298 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{C.-S. Liu} and \textit{L. Qiu}, Numer. Methods Partial Differ. Equations 39, No. 2, 1287--1298 (2023; Zbl 07776963) Full Text: DOI
Keanini, Russell G.; Dahlberg, Jerry; Brown, Philip; Morovati, Mehdi; Moradi, Hamidreza; Jacobs, Donald; Tkacik, Peter T. Stochastic estimation of Green’s functions with application to diffusion and advection-diffusion-reaction problems. (English) Zbl 07736210 Appl. Math. Comput. 457, Article ID 128186, 20 p. (2023). MSC: 60H10 35-01 35R30 35J05 62G05 PDFBibTeX XMLCite \textit{R. G. Keanini} et al., Appl. Math. Comput. 457, Article ID 128186, 20 p. (2023; Zbl 07736210) Full Text: DOI arXiv
Baranchuk, V. A.; Pyatkov, S. G. On some inverse problems of recovering sources in stationary convection-diffusion models. (English) Zbl 1518.35663 Lobachevskii J. Math. 44, No. 3, 1111-1118 (2023). MSC: 35R30 35J25 35N25 PDFBibTeX XMLCite \textit{V. A. Baranchuk} and \textit{S. G. Pyatkov}, Lobachevskii J. Math. 44, No. 3, 1111--1118 (2023; Zbl 1518.35663) Full Text: DOI
Zhang, Hui; Liu, Jijun Solving an inverse source problem by deep neural network method with convergence and error analysis. (English) Zbl 07707674 Inverse Probl. 39, No. 7, Article ID 075013, 29 p. (2023). MSC: 65Nxx 35Rxx 65Jxx PDFBibTeX XMLCite \textit{H. Zhang} and \textit{J. Liu}, Inverse Probl. 39, No. 7, Article ID 075013, 29 p. (2023; Zbl 07707674) Full Text: DOI
Liu, Chein-Shan; Qiu, Lin Solving nonlinear elliptic inverse source, coefficient and conductivity problems by the methods with bases satisfying the boundary conditions automatically. (English) Zbl 07698916 J. Sci. Comput. 95, No. 2, Paper No. 42, 24 p. (2023). MSC: 65Nxx 35Rxx 35Jxx PDFBibTeX XMLCite \textit{C.-S. Liu} and \textit{L. Qiu}, J. Sci. Comput. 95, No. 2, Paper No. 42, 24 p. (2023; Zbl 07698916) Full Text: DOI
Afraites, Lekbir; Masnaoui, Chorouk; Nachaoui, Mourad Shape optimization method for an inverse geometric source problem and stability at critical shape. (English) Zbl 1490.49027 Discrete Contin. Dyn. Syst., Ser. S 15, No. 1, 1-21 (2022). MSC: 49Q10 65N20 35J25 35R35 65N30 PDFBibTeX XMLCite \textit{L. Afraites} et al., Discrete Contin. Dyn. Syst., Ser. S 15, No. 1, 1--21 (2022; Zbl 1490.49027) Full Text: DOI
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 PDFBibTeX XMLCite \textit{G. F. Umbricht}, Math. Model. Anal. 26, No. 3, 339--357 (2021; Zbl 1486.35475) Full Text: DOI
Wen, Jin; Huang, Li-Ming; Liu, Zhuan-Xia A modified quasi-reversibility method for inverse source problem of Poisson equation. (English) Zbl 07480125 Inverse Probl. Sci. Eng. 29, No. 12, 2098-2109 (2021). MSC: 35R30 65N20 PDFBibTeX XMLCite \textit{J. Wen} et al., Inverse Probl. Sci. Eng. 29, No. 12, 2098--2109 (2021; Zbl 07480125) Full Text: DOI
Deng, Xiaomao; Liao, Zi-Ju; Cai, Xiao-Chuan A parallel multilevel domain decomposition method for source identification problems governed by elliptic equations. (English) Zbl 1471.65180 J. Comput. Appl. Math. 392, Article ID 113441, 19 p. (2021). MSC: 65N21 65N55 65K10 65J20 65Y05 49M05 49M27 49M41 65F08 65F10 35J25 93B30 PDFBibTeX XMLCite \textit{X. Deng} et al., J. Comput. Appl. Math. 392, Article ID 113441, 19 p. (2021; Zbl 1471.65180) Full Text: DOI
Min, Tao; Zang, Shunquan; Chen, Shengnan Source strength identification problem for the three-dimensional inverse heat conduction equations. (English) Zbl 1475.65110 Inverse Probl. Sci. Eng. 28, No. 6, 827-838 (2020). MSC: 65M32 65M30 35K05 45D05 35K20 65M80 65J20 65F20 15A18 65R20 65D32 65K10 60H50 35R30 PDFBibTeX XMLCite \textit{T. Min} et al., Inverse Probl. Sci. Eng. 28, No. 6, 827--838 (2020; Zbl 1475.65110) Full Text: DOI
Liu, Chein-Shan An energetic boundary functional method for solving the inverse source problems of 2D nonlinear elliptic equations. (English) Zbl 1464.65166 Eng. Anal. Bound. Elem. 118, 204-215 (2020). MSC: 65N21 PDFBibTeX XMLCite \textit{C.-S. Liu}, Eng. Anal. Bound. Elem. 118, 204--215 (2020; Zbl 1464.65166) Full Text: DOI
Ren, Chunping; Wang, Nengjian; Liu, Qinhui; Liu, Chunsheng Dynamic force identification problem based on a novel improved Tikhonov regularization method. (English) Zbl 1435.65230 Math. Probl. Eng. 2019, Article ID 6095184, 13 p. (2019). MSC: 65R30 35R30 65J20 PDFBibTeX XMLCite \textit{C. Ren} et al., Math. Probl. Eng. 2019, Article ID 6095184, 13 p. (2019; Zbl 1435.65230) Full Text: DOI
Gu, Yan; Lei, Jun; Fan, Chia-Ming; He, Xiao-Qiao The generalized finite difference method for an inverse time-dependent source problem associated with three-dimensional heat equation. (English) Zbl 1403.65039 Eng. Anal. Bound. Elem. 91, 73-81 (2018). MSC: 65M06 65M32 80A23 PDFBibTeX XMLCite \textit{Y. Gu} et al., Eng. Anal. Bound. Elem. 91, 73--81 (2018; Zbl 1403.65039) Full Text: DOI
Liu, Chein-Shan A BIEM using the Trefftz test functions for solving the inverse Cauchy and source recovery problems. (English) Zbl 1403.65121 Eng. Anal. Bound. Elem. 62, 177-185 (2016). MSC: 65N21 65N38 PDFBibTeX XMLCite \textit{C.-S. Liu}, Eng. Anal. Bound. Elem. 62, 177--185 (2016; Zbl 1403.65121) Full Text: DOI
Hamad, A.; Tadi, M. A numerical method for inverse source problems for Poisson and Helmholtz equations. (English) Zbl 1367.65159 Phys. Lett., A 380, No. 44, 3707-3716 (2016). MSC: 65N21 35J05 PDFBibTeX XMLCite \textit{A. Hamad} and \textit{M. Tadi}, Phys. Lett., A 380, No. 44, 3707--3716 (2016; Zbl 1367.65159) Full Text: DOI
Movahedian, Bashir; Boroomand, Bijan Inverse identification of time-harmonic loads acting on thin plates using approximated Green’s functions. (English) Zbl 1348.65176 Inverse Probl. Sci. Eng. 24, No. 8, 1475-1493 (2016). MSC: 65N80 65N21 74K20 PDFBibTeX XMLCite \textit{B. Movahedian} and \textit{B. Boroomand}, Inverse Probl. Sci. Eng. 24, No. 8, 1475--1493 (2016; Zbl 1348.65176) Full Text: DOI
Fogg, Harold J.; Armstrong, Cecil G.; Robinson, Trevor T. Automatic generation of multiblock decompositions of surfaces. (English) Zbl 1352.65606 Int. J. Numer. Methods Eng. 101, No. 13, 965-991 (2015). MSC: 65N50 65D17 PDFBibTeX XMLCite \textit{H. J. Fogg} et al., Int. J. Numer. Methods Eng. 101, No. 13, 965--991 (2015; Zbl 1352.65606) Full Text: DOI Link
Zhao, Jingjun; Liu, Songshu Two regularization methods for inverse source problem on the Poisson equation. (English) Zbl 1323.47009 Complex Var. Elliptic Equ. 60, No. 10, 1374-1391 (2015). MSC: 47A52 65J22 PDFBibTeX XMLCite \textit{J. Zhao} and \textit{S. Liu}, Complex Var. Elliptic Equ. 60, No. 10, 1374--1391 (2015; Zbl 1323.47009) Full Text: DOI
Zhao, Jingjun; Liu, Songshu Central difference regularization method for inverse source problem on the Poisson equation. (English) Zbl 1322.65100 Complex Var. Elliptic Equ. 60, No. 3, 405-415 (2015). Reviewer: Bangti Jin (London) MSC: 65N21 35J05 65N06 35R30 65N12 65N15 PDFBibTeX XMLCite \textit{J. Zhao} and \textit{S. Liu}, Complex Var. Elliptic Equ. 60, No. 3, 405--415 (2015; Zbl 1322.65100) Full Text: DOI
Chang, Joshua C.; Savage, van M.; Chou, Tom A path-integral approach to Bayesian inference for inverse problems using the semiclassical approximation. (English) Zbl 1418.62080 J. Stat. Phys. 157, No. 3, 582-602 (2014). MSC: 62F15 35R30 65C05 65J15 PDFBibTeX XMLCite \textit{J. C. Chang} et al., J. Stat. Phys. 157, No. 3, 582--602 (2014; Zbl 1418.62080) Full Text: DOI arXiv
Yang, Xiao-Mei; Deng, Zhi-Liang A point source identification problem for a time fractional diffusion equation. (English) Zbl 1291.35114 Adv. Math. Phys. 2013, Article ID 485273, 8 p. (2013). MSC: 35K57 35R11 PDFBibTeX XMLCite \textit{X.-M. Yang} and \textit{Z.-L. Deng}, Adv. Math. Phys. 2013, Article ID 485273, 8 p. (2013; Zbl 1291.35114) Full Text: DOI
Gao, Jinghuai; Wang, Dehua; Peng, Jigen A Tikhonov-type regularization method for identifying the unknown source in the modified Helmholtz equation. (English) Zbl 1264.65182 Math. Probl. Eng. 2012, Article ID 878109, 13 p. (2012). MSC: 65N21 78A30 35J05 PDFBibTeX XMLCite \textit{J. Gao} et al., Math. Probl. Eng. 2012, Article ID 878109, 13 p. (2012; Zbl 1264.65182) Full Text: DOI
Ma, Yun-Jie; Fu, Chu-Li; Zhang, Yuan-Xiang Identification of an unknown source depending on both time and space variables by a variational method. (English) Zbl 1252.65106 Appl. Math. Modelling 36, No. 10, 5080-5090 (2012). MSC: 65K10 49N45 PDFBibTeX XMLCite \textit{Y.-J. Ma} et al., Appl. Math. Modelling 36, No. 10, 5080--5090 (2012; Zbl 1252.65106) Full Text: DOI
Li, Ming; Chen, Wen; Tsai, C. H. A regularization method for the approximate particular solution of nonhomogeneous Cauchy problems of elliptic partial differential equations with variable coefficients. (English) Zbl 1245.65150 Eng. Anal. Bound. Elem. 36, No. 3, 274-280 (2012). MSC: 65N20 65J20 35R30 PDFBibTeX XMLCite \textit{M. Li} et al., Eng. Anal. Bound. Elem. 36, No. 3, 274--280 (2012; Zbl 1245.65150) Full Text: DOI
Yang, Fan; Fu, Chu-Li The modified regularization method for identifying the unknown source on Poisson equation. (English) Zbl 1236.35206 Appl. Math. Modelling 36, No. 2, 756-763 (2012). MSC: 35R30 65N21 35J25 35R25 PDFBibTeX XMLCite \textit{F. Yang} and \textit{C.-L. Fu}, Appl. Math. Modelling 36, No. 2, 756--763 (2012; Zbl 1236.35206) Full Text: DOI
Li, Xiao-Xiao; Guo, Heng Zhen; Wan, Shi Min; Yang, Fan Inverse source identification by the modified regularization method on Poisson equation. (English) Zbl 1234.35313 J. Appl. Math. 2012, Article ID 971952, 13 p. (2012). MSC: 35R30 35Q05 35R25 47A52 65F22 PDFBibTeX XMLCite \textit{X.-X. Li} et al., J. Appl. Math. 2012, Article ID 971952, 13 p. (2012; Zbl 1234.35313) Full Text: DOI
Mierzwiczak, M.; Kołodziej, J. A. The determination of heat sources in two dimensional inverse steady heat problems by means of the method of fundamental solutions. (English) Zbl 1269.65117 Inverse Probl. Sci. Eng. 19, No. 6, 777-792 (2011). MSC: 65N21 35R30 35J05 65N80 PDFBibTeX XMLCite \textit{M. Mierzwiczak} and \textit{J. A. Kołodziej}, Inverse Probl. Sci. Eng. 19, No. 6, 777--792 (2011; Zbl 1269.65117) 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 PDFBibTeX XMLCite \textit{M. Mierzwiczak} and \textit{J. A. Kołodziej}, Comput. Phys. Commun. 181, No. 12, 2035--2043 (2010; Zbl 1219.65101) Full Text: DOI