Recovering a general space-time-dependent heat source by the coupled boundary integral equation method

References

• E. G. Savateev and P. Duchateau, On Problems of Determining the Source Function in a Parabolic Equation, J. Inv. Ill-Posed Prob., vol. 3, pp. 83–102, 1995.
   Google Scholar
• J. R. Cannon and P. Duchateau, Structural Identification of an Unknown Source Term in a Heat Equation, Inv. Prob., vol. 14, pp. 535–551, 1998.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• L. Ling, M. Yamamoto, and Y. C. Hon, Identification of Source Locations in Two-Dimensional Heat Equations, Inv. Prob., vol. 22, pp. 1289–1305, 2006.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• A. Hazanee, M. I. Ismailov, D. Lesnic, and N. B. Kerimov, An Inverse Time-Dependent Source Problem for the Heat Equation, Appl. Num. Math., vol. 69, pp. 13–33, 2013.
   Web of Science ®Google Scholar
• W. Wang, B. Han, and M. Yamamoto, Inverse Heat Problem of Determining Time-Dependent Source Parameter in Reproducing Kernel Space, Nonl. Anal. Real World Appl., vol. 14, pp. 875–887, 2013.
   Web of Science ®Google Scholar
• F. Yang and C. L. Fu, A Mollification Regularization Method for the Inverse Spatial-Dependent Heat Source Problem, J. Comput. Appl. Math., vol. 255, pp. 555–567, 2014.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• C.-S. Liu, An Iterative Algorithm for Identifying Heat Source by Using a DQ and a Lie-Group Method, Inv. Prob. Sci. Eng., vol. 23, pp. 67–92, 2015.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• 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, Num. Heat Transfer B, vol. 67, pp 231–254, 2015.
   Google Scholar
• M. Dehghan, Identification of a Time Dependent Coefficient in a Partial Differential Equation Subject to an Extra Measurement, Num. Meth. Partial Diff. Eqs., vol. 21, pp. 611–622, 2005.
   Web of Science ®Google Scholar
• C.-S. Liu, A two-stage LGSM to Identify Time-dependent Heat Source Through an Internal Measurement of Temperature, Int. J. Heat Mass Transfer, vol. 52, pp. 1635–1642, 2009.
   Web of Science ®Google Scholar
• W. Yeih and C.-S. Liu, A Three-point BVP of Time-dependent Inverse Heat Source Problems and Solving by a TSLGSM, Comput. Model. Eng. Sci., vol. 46, pp. 107–127, 2009.
   Web of Science ®Google Scholar
• C. L. Kuo, J. R. Chang, and C.-S. Liu, The Modified Polynomial Expansion Method for Solving the Inverse Heat Source Problems, Num. Heat Transfer B, vol. 63, pp. 357–370, 2013.
   Web of Science ®Google Scholar
• C.-S. Liu, Lie-group Differential Algebraic Equations Method to Recover Heat Source in a Cauchy Problem with Analytic Continuation Data, Int. J. Heat Mass Transfer, vol. 78, pp. 538–547, 2014.
   Web of Science ®Google Scholar
• C.-S. Liu, A Lie-group Shooting Method for Reconstructing a Past Time-Dependent Heat Source, Int. J. Heat Mass Transfer, vol. 55, pp. 1773–1781, 2012.
   Web of Science ®Google Scholar
• C.-S. Liu, On-line Detecting Heat Source of a Nonlinear Heat Conduction Equation by a Differential Algebraic Equation Method, Int. J. Heat Mass Transfer, vol. 76, pp. 153–161, 2014.
   Web of Science ®Google Scholar
• C.-S. Liu, To Recover Heat Source G(x) + H(t) by Using Homogeneized Function and Solving Rectangular Differencing Equations, Num. Heat Transfer B, vol. 69, pp. 351–363, 2016.
   Web of Science ®Google Scholar
• C.-S. Liu and C. W. Chang, A Global Boundary Integral Equation Method for Recovering Space-Time Dependent Heat Source, Int. J. Heat Mass Transfer, vol. 92, pp. 1034–1040, 2016.
   Web of Science ®Google Scholar
• 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, 943–953, 2016.
   Web of Science ®Google Scholar
• C.-S. Liu, Homogenized Functions to Recover H(t)/H(x) by Solving a Small Scale Linear System of Differencing Equations, Int. J. Heat Mass Transfer, vol. 101, pp. 1103–1110, 2016.
   Web of Science ®Google Scholar
• C.-S. Liu, A Two-side Equilibration Method to Reduce the Condition Number of an Ill-Posed Linear System, Comput. Model. Eng. Sci., vol. 91, pp. 17–42, 2013.
   Web of Science ®Google Scholar
• C.-S. Liu, An Equilibrated Method of Fundamental Solutions to Choose the Best Source Points for the Laplace Equation, Eng. Anal. Bound. Elem., vol. 36, pp. 1235–1245, 2012.
   Web of Science ®Google Scholar
• C.-S. Liu, Optimally Scaled Vector Regularization Method to Solve Ill-Posed Linear Problems, Appl. Math. Comput., vol. 218, pp. 10602–10616, 2012.
   Web of Science ®Google Scholar
• C.-S. Liu, The Pre/post Equilibrated Conditioning Methods to Solve Cauchy Problems, Eng. Anal. Bound. Elem., vol. 40, pp. 62–70, 2014.
   Web of Science ®Google Scholar