참고문헌
- K. A. Ames, G. W. Clark, J. F. Epperson, and S. F. Oppenhermer, A comparison of regularizations for an ill-posed problem, Math. Comp. 67 (1998), no. 224, 1451–-1471 https://doi.org/10.1090/S0025-5718-98-01014-X
- L. Elden, F. Berntsson, and T. Reginska, Wavelet and Fourier methods for solving the sideways heat equation, SIAM J. Sci. Comput. 21 (2000), no. 6, 2187–-2205 https://doi.org/10.1137/S1064827597331394
- H. W. Engl, M. Hanke, and A. Neubauer, Regularization of inverse problems, Mathematics and its Applications, 375. Kluwer Academic Publishers Group, Dordrecht, 1996
- L. C. Evans, Partial differential equations, Graduate Studies in Mathematics 19, American Mathematical Society, Providence, RI, 1998
- D. N. Hao, A mollification method for ill-posed problems, Numer. Math. 68 (1994), no. 4, 469–-506 https://doi.org/10.1007/s002110050073
- T. Hohage, Regularization of exponentially ill-posed problems, Numer. Funct. Anal. Optim. 21 (2000), no. 3-4, 439–-464 https://doi.org/10.1080/01630560008816965
- M. Jourhmane and N. S. Mera, An iterative algorithm for the backward heat conduction problem based on variable relaxtion factors, Inverse Probl. Sci. Eng. 10 (2002), no. 4, 293–-308 https://doi.org/10.1080/10682760290004320
- S. M. Kirkup and M. Wadsworth, Solution of inverse diffusion problems by operatorsplitting methods, Applied Mathematical Modelling 26 (2002), no. 10, 1003–-1018 https://doi.org/10.1016/S0307-904X(02)00053-7
- R. Lattes and J. L. Lions, Methode de quasi-reversibilite et applications, Travaux et Recherches Mathematiques, No. 15 Dunod, Paris 1967
- P. Mathe and S. Pereverzev, Geometry of ill-posed problems in variable Hilbert Scales, Inverse Problems 19 (2003), 789–-803 https://doi.org/10.1088/0266-5611/19/3/319
- N. S. Mera, L. Elliott, D. B. Ingham, and D. Lesnic, An iterative boundary element method for solving the one-dimensional backward heat conduction problem, International Journal of Heat and Mass Transfer 44 (2001), no. 10, 1937-1946 https://doi.org/10.1016/S0017-9310(00)00235-0
- N. S. Mera, The method of fundamental solutions for the backward heat conduction problem, Inverse Probl. Sci. Eng. 13 (2005), no. 1, 65-78 https://doi.org/10.1080/10682760410001710141
- K. Miller, Stabilized quasi-reversibility and other nearly-best-possible methods for nonwell- posed problems, Symposium on Non-Well-Posed Problems and Logarithmic Convexity (Heriot-Watt Univ., Edinburgh, 1972), pp. 161–176. Lecture Notes in Math., Vol. 316, Springer, Berlin, 1973
- R. E. Showalter, The final value problem for evolution equations, J. Math. Anal. Appl. 47 (1974), 563-572 https://doi.org/10.1016/0022-247X(74)90008-0
- U. Tautenhahn, Optimal stable approximations for the sideways heat equation, J. Inverse Ill-Posed Probl. 5 (1997), no. 3, 287-307 https://doi.org/10.1515/jiip.1997.5.3.287
- U. Tautenhahn, Optimality for ill-posed problems under general source conditions, Numer. Funct. Anal. Optim. 19 (1998), no. 3-4, 377–-398 https://doi.org/10.1080/01630569808816834
- U. Tautenhahn and T. Schroter, On optimal regularization methods for the backward heat equation, Z. Anal. Anwendungen 15 (1996), no. 2, 475-493 https://doi.org/10.4171/ZAA/711
피인용 문헌
- Spectral method for ill-posed problems based on the balancing principle vol.23, pp.2, 2015, https://doi.org/10.1080/17415977.2014.894039
- A multiple/scale/direction polynomial Trefftz method for solving the BHCP in high-dimensional arbitrary simply-connected domains vol.92, 2016, https://doi.org/10.1016/j.ijheatmasstransfer.2015.09.057
- A self-adaptive LGSM to recover initial condition or heat source of one-dimensional heat conduction equation by using only minimal boundary thermal data vol.54, pp.7-8, 2011, https://doi.org/10.1016/j.ijheatmasstransfer.2010.12.013
- A highly accurate LGSM for severely ill-posed BHCP under a large noise on the final time data vol.53, pp.19-20, 2010, https://doi.org/10.1016/j.ijheatmasstransfer.2010.05.036
- The multiple-scale polynomial Trefftz method for solving inverse heat conduction problems vol.95, 2016, https://doi.org/10.1016/j.ijheatmasstransfer.2016.01.008
- The Method of Fundamental Solutions for Solving the Backward Heat Conduction Problem with Conditioning by a New Post-Conditioner vol.60, pp.1, 2011, https://doi.org/10.1080/10407790.2011.588134
- Conditional Stability Estimates for Ill-Posed PDE Problems by Using Interpolation vol.34, pp.12, 2013, https://doi.org/10.1080/01630563.2013.819515
- Numerically solving twofold ill-posed inverse problems of heat equation by the adjoint Trefftz method vol.73, pp.1, 2018, https://doi.org/10.1080/10407790.2017.1420317