References
- J. R. Cannon and P. Duchateau, “Structural identification of an unknown source term in a heat equation,” Inverse Prob., vol. 14, pp. 535–551, 1998.
- E. G. Savateev and P. Duchateau, “On problems of determining the source function in a parabolic equation,” J. Inverse Ill-Posed Prob., vol. 3, pp. 83–102, 1995.
- V. T. Borukhov and P. N. Vabishchevich, “Numerical solution of the inverse problem of reconstructing a distributed right-hand side of a parabolic equation,” Comput. Phys. Commun., vol. 126, pp. 32–36, 2000.
- A. Farcas and D. Lesnic, “The boundary-element method for the determination of a heat source dependent on one variable,” J. Eng. Math., vol. 54, pp. 375–388, 2006.
- L. Ling, M. Yamamoto, and Y. C. Hon, “Identification of source locations in two-dimensional heat equations,” Inverse Prob., vol. 22, pp. 1289–1305, 2006.
- L. Yan, C.-L. Fu, and F.-L. Yang, “The method of fundamental solutions for the inverse heat source problem,” Eng. Anal. Bound. Elem., vol. 32, pp. 216–222, 2008.
- F. Yang and C.-L. Fu, “The method of simplified Tikhonov regularization for dealing with the inverse time-dependent heat source problem,” Comput. Math. Appl., vol. 60, pp. 1228–1236, 2010.
- L. Yang, M. Dehghan, J.-N. Yu, and G.-W. Luo, “Inverse problem of time-dependent heat sources numerical reconstruction,” Math. Comput. Simul., vol. 81, pp. 1656–1672, 2011.
- C.-S. Liu, “An iterative algorithm for identifying heat source by using a DQ and a Lie-group method,” Inverse Prob. Sci. Eng., vol. 23, pp. 67–92, 2015.
- C.-S. Liu, “Finding unknown heat source in a nonlinear Cauchy problem by the Lie-group differential algebraic equations method,” Eng. Anal. Bound. Elem., vol. 50, pp. 148–156, 2015.
- C.-S. Liu, C.-L. Kuo, and J.-R. Chang, “Recovering a heat source and initial value by a Lie-group differential algebraic equations method,” Numer. Heat Transfer B, vol. 67, pp. 231–254, 2015.
- Y. Wang, J. Cheng, J. Nakagawa, and M. Yamamoto, “A numerical method for solving the inverse heat conduction problem without initial value,” Inverse Prob. Sci. Eng., vol. 18, pp. 655–671, 2010.
- C.-S. Liu, “An LGDAE method to solve nonlinear Cauchy problem without initial temperature,” Comput. Model. Eng. Sci., vol. 99, pp. 371–391, 2014.
- J.-C. Liu and T. Wei, “A quasi-reversibility regularization method for an inverse heat conduction problem without initial data,” Appl. Math. Comput., vol. 219, pp. 10866–10881, 2013.
- J.-C. Liu and J.-G. Wang, “Cauchy problem for the heat equation in a bounded domain without initial value,” Comput. Model. Eng. Sci., vol. 97, pp. 437–462, 2014.
- C.-S. Liu and C.-W. Chang, “A simple algorithm for solving Cauchy problem of nonlinear heat equation without initial value,” Int. J. Heat Mass Transfer, vol. 80, pp. 562–569, 2015.
- B.-T. Johansson and D. Lesnic, “A procedure for determining a spacewise dependent heat source and the initial temperature,” Appl. Anal., vol. 87, pp. 265–276, 2008.
- T. Wei and J.-C. Wang, “Simultaneous determination for a space-dependent heat source and the initial data by the MFS,” Eng. Anal. Bound. Elem., vol. 36, pp. 1848–1853, 2012.
- C.-S. Liu, “A self-adaptive LGSM to recover initial condition or heat source of one-dimensional heat conduction equation by using only minimal boundary thermal data,” Int. J. Heat Mass Transfer, vol. 54, pp. 1305–1312, 2011.
- C.-S. Liu, “An integral equation method to recover non-additive and non-separable heat source without initial temperature,” Int. J. Heat Mass Transfer, vol. 97, pp. 943–953, 2016.