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Research Article

An inverse source identification by nonlinear optimization in a two-dimensional hyperbolic problem

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Pages 2110-2130 | Received 09 Sep 2020, Accepted 08 Mar 2021, Published online: 11 Apr 2021

References

  • Aki K, Richards PG. Quantitative seismology theory and methods. New York: Freeman; 1980.
  • Evans LC. Partial differential equations, 2nd edn. Graduate studies in mathematics, vol. 19. New York: American Mathematical Society; 2002.
  • Kuliev GF. Problem of optimal control of the coefficients for hyperbolic equations. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 1985;3:39–44.
  • Feng X, Sutton B, Leuhart S, et al. Identification problem for the wave equation with Neumann data input and Dirichlet data abservating. Nonlinear Anal. 2003;52(7):1777–1795.
  • Maciąg A. The usage of wave polynomials in solving direct and inverse problems for two-dimensional wave equation. Int J Numer Method Biomed Eng. 2011;27(7):1107–1125.
  • Tagiyev RK. On optimal control of the hyperbolic equation coefficients. Autom Remote Control. 2012;73(7):1145–1155.
  • Hasanov A, Mukanova B. Relationship between representation formulas for unique regularized solutions of inverse source problems with final overdetermination and singular value decomposition of input–output operators. IMA J Appl Math. 2015;80:676–696.
  • Subaşı M, Kaçar A. A variational technique for optimal boundary control in a hyperbolic problem. Appl Math Comput. 2012;218:6629–6636.
  • Deiveegan A, Prakash P, Nieto JJ. Optimization method for identifying the source term in an inverse Wave equation. Electron J Diff Equat. 2017;2017(200):1–15.
  • Subaşı M, Araz S. Numerical regularization of optimal control for the coefficient function in a wave equation. Iran J Sci Technol Trans A Sci. 2019;43:2325–2333.
  • Eng HW, Scherzer O, Yamamato M. Uniqueness and stable determination of forcing terms in linear partial differential equations with overspecified boundary data. Inverse Probl. 1994;10:1253–1276.
  • Yamamato M. On ill-posedness and a Tikhonov regularization for a multidimensional inverse hyperbolic problem. J Math Kyoto Univ. 1996;36:825–856.
  • Cheng J, Yamamato M. One new strategy for a priori choice of regularization parameters in Tikhonov’s regularization. Inverse Probl. 2000;16:L31–L38.
  • Kabanikhin SI, Satybaev AD, Shishlenin MA. Direct methods of solving multidimensional inverse hyperbolic problems. Utrecht: VSP Science Press; 2005.
  • Larson MG, Bengzon F. The finite element method: theory, implementation, and applications. Berlin: Springer; 2010.
  • Levenberg K. A method for the solution of certain nonlinear problems in least squares. Qart Appl Math. 1944;2:164–166.
  • Marquardt DW. An algorithm for least-squares estimation of nonlinear inequalities. SIAM J Appl Math. 1963;11:431–441.
  • Goldfeld SM, Quandt RE, Trotter HF. Maximization by quadratic hill-climbing. Econometrica. 1966;34(3):541–551.
  • Sorensen DC. Newton's method with a model trust region modification. SIAM J Numer Anal. 1982;19(2):409–426.
  • Conn AR, Gould NIM, Toint PL. Trust-region methods. Philadelphia: Society for Industrial and Applied Mathematics; 2000.
  • Madsen K, Nielsen HB, Tingleff O. Methods for non-linear least squares problems, informatics and mathematical modelling. Kopenhag: Technical University of Denmark; 2004.

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