Tuan, Nguyen Huy; Nane, Erkan; Trong, Dang Duc Analysis of a quasi-reversibility method for nonlinear parabolic equations with uncertainty data. (English) Zbl 1482.35278 Ill. J. Math. 65, No. 4, 793-845 (2021). MSC: 35R30 35K20 35K59 35R60 47H10 47J06 PDFBibTeX XMLCite \textit{N. H. Tuan} et al., Ill. J. Math. 65, No. 4, 793--845 (2021; Zbl 1482.35278) Full Text: DOI Link
Dien, Nguyen Minh; Trong, Dang Duc On the nonlinear generalized Langevin equation involving \(\psi\)-Caputo fractional derivatives. (English) Zbl 1493.34021 Fractals 29, No. 6, Article ID 2150128, 20 p. (2021). MSC: 34A08 34A34 34G20 26A33 47N20 PDFBibTeX XMLCite \textit{N. M. Dien} and \textit{D. D. Trong}, Fractals 29, No. 6, Article ID 2150128, 20 p. (2021; Zbl 1493.34021) Full Text: DOI
Dien, Nguyen Minh; Trong, Dang Duc The backward problem for nonlinear fractional diffusion equation with time-dependent order. (English) Zbl 1471.35328 Bull. Malays. Math. Sci. Soc. (2) 44, No. 5, 3345-3359 (2021). MSC: 35R30 35K90 35R11 65F22 PDFBibTeX XMLCite \textit{N. M. Dien} and \textit{D. D. Trong}, Bull. Malays. Math. Sci. Soc. (2) 44, No. 5, 3345--3359 (2021; Zbl 1471.35328) Full Text: DOI
Trong, Dang Duc; Hai, Dinh Nguyen Duy Backward problem for time-space fractional diffusion equations in Hilbert scales. (English) Zbl 1524.35722 Comput. Math. Appl. 93, 253-264 (2021). MSC: 35R11 35R30 35R25 65M32 35K05 PDFBibTeX XMLCite \textit{D. D. Trong} and \textit{D. N. D. Hai}, Comput. Math. Appl. 93, 253--264 (2021; Zbl 1524.35722) Full Text: DOI
Trong, Dang Duc; Dien, Nguyen Minh; Viet, Tran Quoc Global solution of space-fractional diffusion equations with nonlinear reaction source terms. (English) Zbl 1450.35281 Appl. Anal. 99, No. 15, 2707-2737 (2020). MSC: 35R11 35R25 35R30 35K15 35K57 65J20 PDFBibTeX XMLCite \textit{D. D. Trong} et al., Appl. Anal. 99, No. 15, 2707--2737 (2020; Zbl 1450.35281) Full Text: DOI
Dien, Nguyen Minh; Hai, Dinh Nguyen Duy; Viet, Tran Quoc; Trong, Dang Duc On Tikhonov’s method and optimal error bound for inverse source problem for a time-fractional diffusion equation. (English) Zbl 1445.35328 Comput. Math. Appl. 80, No. 1, 61-81 (2020). MSC: 35R30 35R25 35R11 49K20 35K15 PDFBibTeX XMLCite \textit{N. M. Dien} et al., Comput. Math. Appl. 80, No. 1, 61--81 (2020; Zbl 1445.35328) Full Text: DOI
Hai, Dinh Nguyen Duy; Trong, Dang Duc Optimal error bound and truncation regularization method for a backward time-fractional diffusion problem in Hilbert scales. (English) Zbl 1440.65088 Appl. Math. Lett. 107, Article ID 106448, 8 p. (2020). MSC: 65M06 65M30 65M15 65J20 26A33 35R11 PDFBibTeX XMLCite \textit{D. N. D. Hai} and \textit{D. D. Trong}, Appl. Math. Lett. 107, Article ID 106448, 8 p. (2020; Zbl 1440.65088) Full Text: DOI
Trong, Dang Duc; Hai, Dinh Nguyen Duy; Dien, Nguyen Minh On a time-space fractional backward diffusion problem with inexact orders. (English) Zbl 1442.35527 Comput. Math. Appl. 78, No. 5, 1572-1593 (2019). MSC: 35R11 35B30 PDFBibTeX XMLCite \textit{D. D. Trong} et al., Comput. Math. Appl. 78, No. 5, 1572--1593 (2019; Zbl 1442.35527) Full Text: DOI
Trong, Dang Duc; Hai, Dinh Nguyen Duy; Minh, Nguyen Dang Stepwise regularization method for a nonlinear Riesz-Feller space-fractional backward diffusion problem. (English) Zbl 1431.65157 J. Inverse Ill-Posed Probl. 27, No. 6, 759-775 (2019). MSC: 65M32 35R30 47A52 35R11 65M30 PDFBibTeX XMLCite \textit{D. D. Trong} et al., J. Inverse Ill-Posed Probl. 27, No. 6, 759--775 (2019; Zbl 1431.65157) Full Text: DOI
Trong, Dang Duc; Hai, Dinh Nguyen Duy; Nguyen, Dang Minh Optimal regularization for an unknown source of space-fractional diffusion equation. (English) Zbl 1429.65221 Appl. Math. Comput. 349, 184-206 (2019). MSC: 65M32 35R11 47A52 PDFBibTeX XMLCite \textit{D. D. Trong} et al., Appl. Math. Comput. 349, 184--206 (2019; Zbl 1429.65221) Full Text: DOI
Viet, Tran Quoc; Dien, Nguyen Minh; Trong, Dang Duc Stability of solutions of a class of nonlinear fractional Laplacian parabolic problems. (English) Zbl 1419.35228 J. Comput. Appl. Math. 355, 51-76 (2019). MSC: 35R11 PDFBibTeX XMLCite \textit{T. Q. Viet} et al., J. Comput. Appl. Math. 355, 51--76 (2019; Zbl 1419.35228) Full Text: DOI
Dang Duc Trong; Dinh Ngoc Thanh; Nguyen Nhu Lan Regularization for the inverse problem of finding the purely time-dependent volatility. (English) Zbl 1349.91315 Vietnam J. Math. 44, No. 3, 513-530 (2016). MSC: 91G60 35R30 65M32 91G20 PDFBibTeX XMLCite \textit{Dang Duc Trong} et al., Vietnam J. Math. 44, No. 3, 513--530 (2016; Zbl 1349.91315) Full Text: DOI
Trong, Dang Duc; Duy, Bui Thanh; Minh, Mach Nguyet Backward heat equations with locally Lipschitz source. (English) Zbl 1331.35393 Appl. Anal. 94, No. 10, 2023-2036 (2015). MSC: 35R30 35K05 35R25 35A22 PDFBibTeX XMLCite \textit{D. D. Trong} et al., Appl. Anal. 94, No. 10, 2023--2036 (2015; Zbl 1331.35393) Full Text: DOI
Dang Duc Trong; Dinh Ngoc Thanh; Nguyen Nhu Lan; Pham Hoang Uyen Calibration of the purely \(t\)-dependent Black-Scholes implied volatility. (English) Zbl 1291.91213 Appl. Anal. 93, No. 4, 859-874 (2014). MSC: 91G20 91G60 45Q05 65M32 PDFBibTeX XMLCite \textit{Dang Duc Trong} et al., Appl. Anal. 93, No. 4, 859--874 (2014; Zbl 1291.91213) Full Text: DOI
Dang Duc Trong; Phan Thanh Nam; Phung Trong Thuc The body force in a three-dimensional Lamé system: identification and regularization. (English) Zbl 1398.74021 Inverse Probl. Sci. Eng. 20, No. 4, 517-532 (2012). MSC: 74B05 74H10 PDFBibTeX XMLCite \textit{Dang Duc Trong} et al., Inverse Probl. Sci. Eng. 20, No. 4, 517--532 (2012; Zbl 1398.74021) Full Text: DOI arXiv
Quan, Pham Hoang; Trong, Dang Duc; Triet, Le Minh; Tuan, Nguyen Huy A modified quasi-boundary value method for regularizing of a backward problem with time-dependent coefficient. (English) Zbl 1227.65089 Inverse Probl. Sci. Eng. 19, No. 3, 409-423 (2011). Reviewer: Robert Plato (Siegen) MSC: 65M30 35K05 PDFBibTeX XMLCite \textit{P. H. Quan} et al., Inverse Probl. Sci. Eng. 19, No. 3, 409--423 (2011; Zbl 1227.65089) Full Text: DOI
Tuan, Nguyen Huy; Trong, Dang Duc Two regularization methods for backward heat problems with new error estimates. (English) Zbl 1219.35370 Nonlinear Anal., Real World Appl. 12, No. 3, 1720-1732 (2011). Reviewer: Elena V. Tabarintseva (Chelyabinsk) MSC: 35R30 65M30 65M15 PDFBibTeX XMLCite \textit{N. H. Tuan} and \textit{D. D. Trong}, Nonlinear Anal., Real World Appl. 12, No. 3, 1720--1732 (2011; Zbl 1219.35370) Full Text: DOI
Nguyen Huy Tuan; Pham Hoang Quan; Dang Duc Trong; Nguyen Do Minh Nhat A nonlinear backward parabolic problem: regularization by quasi-reversibility and error estimates. (English) Zbl 1223.35186 Asian-Eur. J. Math. 4, No. 1, 145-161 (2011). Reviewer: Radu Precup (Cluj-Napoca) MSC: 35K05 35K99 47J06 35R25 35K58 35K90 PDFBibTeX XMLCite \textit{Nguyen Huy Tuan} et al., Asian-Eur. J. Math. 4, No. 1, 145--161 (2011; Zbl 1223.35186) Full Text: DOI
Tuan, Nguyen Huy; Trong, Dang Duc; Quan, Pham Hoang A modified integral equation method of the semilinear backward heat problem. (English) Zbl 1416.65310 Appl. Math. Comput. 217, No. 12, 5177-5185 (2011). MSC: 65M30 35Q79 35R30 PDFBibTeX XMLCite \textit{N. H. Tuan} et al., Appl. Math. Comput. 217, No. 12, 5177--5185 (2011; Zbl 1416.65310) Full Text: DOI
Dang Duc Trong; Mach Nguyet Minh; Pham Ngoc Dinh, Alain; Phan Thanh Nam Hölder-type approximation for the spatial source term of a backward heat equation. (English) Zbl 1208.35168 Numer. Funct. Anal. Optim. 31, No. 12, 1386-1405 (2010). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 35R30 35K05 65N21 65D05 PDFBibTeX XMLCite \textit{Dang Duc Trong} et al., Numer. Funct. Anal. Optim. 31, No. 12, 1386--1405 (2010; Zbl 1208.35168) Full Text: DOI
Tuan, Nguyen Huy; Trong, Dang Duc Sharp estimates for approximations to a nonlinear backward heat equation. (English) Zbl 1200.35317 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 11, 3479-3488 (2010). MSC: 35R25 35K05 35A35 47J06 47H10 PDFBibTeX XMLCite \textit{N. H. Tuan} and \textit{D. D. Trong}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 11, 3479--3488 (2010; Zbl 1200.35317) Full Text: DOI
Tuan, Nguyen Huy; Trong, Dang Duc A nonlinear parabolic equation backward in time: regularization with new error estimates. (English) Zbl 1196.35225 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 6, 1842-1852 (2010). MSC: 35R25 35K55 47J06 47H10 PDFBibTeX XMLCite \textit{N. H. Tuan} and \textit{D. D. Trong}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 6, 1842--1852 (2010; Zbl 1196.35225) Full Text: DOI
Quan, P. H.; Trong, D. D.; Tuan, N. H. A new version of quasi-boundary value method for a 1-D nonlinear ill-posed heat problem. (English) Zbl 1184.35311 J. Inverse Ill-Posed Probl. 17, No. 9, 913-932 (2009). MSC: 35R25 35K05 47J06 47N20 65M30 PDFBibTeX XMLCite \textit{P. H. Quan} et al., J. Inverse Ill-Posed Probl. 17, No. 9, 913--932 (2009; Zbl 1184.35311) Full Text: DOI
Dang Duc Trong; Pham Ngoc Dinh, Alain; Phan Thanh Nam Determine the special term of a two-dimensional heat source. (English) Zbl 1172.35409 Appl. Anal. 88, No. 3, 457-474 (2009). MSC: 35K05 35R25 35K20 PDFBibTeX XMLCite \textit{Dang Duc Trong} et al., Appl. Anal. 88, No. 3, 457--474 (2009; Zbl 1172.35409) Full Text: DOI arXiv
Trong, Dang Duc; Tuan, Nguyen Huy Regularization and error estimate for the nonlinear backward heat problem using a method of integral equation. (English) Zbl 1172.35517 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 9, 4167-4176 (2009). MSC: 35R30 35A35 35B45 PDFBibTeX XMLCite \textit{D. D. Trong} and \textit{N. H. Tuan}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 9, 4167--4176 (2009; Zbl 1172.35517) Full Text: DOI
Dang Duc Trong; Pham Ngoc Dinh, Alain; Phan Thanh Nam; Truong Trung Tuyen Determination of the body force of a two-dimensional isotropic elastic body. (English) Zbl 1163.74005 J. Comput. Appl. Math. 229, No. 1, 192-207 (2009). MSC: 74B05 35R30 35R25 PDFBibTeX XMLCite \textit{Dang Duc Trong} et al., J. Comput. Appl. Math. 229, No. 1, 192--207 (2009; Zbl 1163.74005) Full Text: DOI arXiv
Pham Hoang Quan; Dang Duc Trong; Pham Ngoc Dinh, Alain A nonlinearly ill-posed problem of reconstructing the temperature from interior data. (English) Zbl 1154.47056 Numer. Funct. Anal. Optim. 29, No. 3-4, 445-469 (2008). Reviewer: Wojciech Kryszewski (Toruń) MSC: 47N20 47J06 35J60 42A38 47H10 PDFBibTeX XMLCite \textit{Pham Hoang Quan} et al., Numer. Funct. Anal. Optim. 29, No. 3--4, 445--469 (2008; Zbl 1154.47056) Full Text: DOI arXiv
Trong, Dang Duc; Quan, Pham Hoang; Khanh, Tran Vu; Tuan, Nguyen Huy A nonlinear case of the 1-D backward heat problem: regularization and error estimate. (English) Zbl 1246.35104 Z. Anal. Anwend. 26, No. 2, 231-245 (2007). MSC: 35K55 35B10 35B30 35R25 47N20 80A20 PDFBibTeX XMLCite \textit{D. D. Trong} et al., Z. Anal. Anwend. 26, No. 2, 231--245 (2007; Zbl 1246.35104) Full Text: DOI
Quan, Pham Hoang; Trong, Dang Duc A nonlinearly backward heat problem: uniqueness, regularization and error estimate. (English) Zbl 1099.35045 Appl. Anal. 85, No. 6-7, 641-657 (2006). MSC: 35K55 47J06 47H10 35R25 35K15 PDFBibTeX XMLCite \textit{P. H. Quan} and \textit{D. D. Trong}, Appl. Anal. 85, No. 6--7, 641--657 (2006; Zbl 1099.35045) Full Text: DOI
Matsuura, T.; Saitoh, S.; Trong, D. D. Approximate and analytical inversion formulas in heat conduction on multidimensional spaces. (English) Zbl 1095.35072 J. Inverse Ill-Posed Probl. 13, No. 3-6, 479-493 (2005). MSC: 35R30 35K05 35-04 PDFBibTeX XMLCite \textit{T. Matsuura} et al., J. Inverse Ill-Posed Probl. 13, No. 3--6, 479--493 (2005; Zbl 1095.35072) Full Text: DOI