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Articles

Identifying unknown source in degenerate parabolic equation from final observation

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Pages 1012-1031 | Received 15 Nov 2019, Accepted 24 Aug 2020, Published online: 15 Sep 2020

References

  • Buchot JM, Raymond JP. A linearized model for boundary layer equations. Optimal control of complex structures (Oberwolfach, 2000). Basel: BirkhNauser; 2002; p. 3–42. (Internat. Ser. Numer. Math.; 139).
  • Cannarsa P, Martinez P, Vancostenoble J. Null controllability of degenerate heat equations. Adv Differ Equ. 2005;10:153–190.
  • Cannarsa P, Martinez P, Vancostenoble J. Carleman estimates for a class of degenerate parabolic operators. SIAM J Control Optim. 2008;47:1–19. doi: 10.1137/04062062X
  • Cannarsa P, Tort J, Yamamoto M. Determination of source terms in a degenerate parabolic equation. Inverse Probl. 2010;26:105003. (20pp) doi: 10.1088/0266-5611/26/10/105003
  • Choulli M, Yamamoto M. Generic well-posedness of a linear inverse parabolic problem with diffusion parameters. J Inverse and Ill-Posed Prob. 1999;7(3):241–254.
  • Deng ZC, Qian K, Rao XB, et al. An inverse problem of identifying the source coefficient in a degenerate heat equation. Inverse Probl Sci Eng. 2015;23(3):498–517. doi: 10.1080/17415977.2014.922079
  • Deng ZC, Yang L. An inverse problem of identifying the coefficient of first-order in a degenerate parabolic equation. J Comput Appl Math. 2011;235(15):4404–4417. doi: 10.1016/j.cam.2011.04.006
  • Egger H, Engl HW. Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates. Inverse Problems. 2005;21:1027–1045. doi: 10.1088/0266-5611/21/3/014
  • Fotouhi M, Salimi L. Null controllability of degenerate/singular parabolic equations. J Dyn Control Syst. 2012;18(4):573–602. doi: 10.1007/s10883-012-9160-5
  • Hasanov A, Slodička M. An analysis of inverse source problems with final time measured output data for the heat conduction equation: A semigroup approach. Appl Math Lett. 2013;26(2):207–214. doi: 10.1016/j.aml.2012.08.013
  • Isakov V. Inverse parabolic problems with the final overdetermination. Commun Pure Appl Math. 1991;44(2):185–209. doi: 10.1002/cpa.3160440203
  • Jiang LS, Tao YS. Identifying the volatility of underlying assets from option prices. Inverse Probl. 2001;17:137–155. doi: 10.1088/0266-5611/17/1/311
  • Li G, Yamamoto M. Stability analysis for determining a source term in a 1-D advection-dispersion equation. J. Inv. Ill-posed Problems. 200614(2):147–155. doi: 10.1515/156939406777571067
  • Martinez P, Raymond JP, Vancostenoble J. Regional null controllability of a linearized Crocco-type equation. SIAM J Control Optim. 2003;42:709–728. doi: 10.1137/S0363012902403547
  • Oleinik AO, Samokhin VN. Mathematical models in boundary layer theory. Chapman and Hall/CRC; 1999.
  • Rundell W, Colton DL. Determination of an unknown non-homogeneous term in a linear partial differential equation, from overspecified boundary data. Applicable Anal. 1980;10(3):231–242. doi: 10.1080/00036818008839304
  • Rudin W. Real and complex analysis. Singapore: Tata McGraw-Hill Education; 1987.
  • Tort J. Determination of source terms in a degenerate parabolic equation from a locally distributed observation. C R Acad Sci Paris, Ser I. 2010;348:1287–1291. doi: 10.1016/j.crma.2010.10.031
  • Tort J, Vancostenoble J. Determination of the insolation function in the nonlinear sellers climate model. Ann I H Poincare-AN. 2012;29:683–713. doi: 10.1016/j.anihpc.2012.03.003
  • Rao XB, Wang YX, Qian K. Numerical simulation for an inverse source problem in a degenerate parabolic equation. Appl Math Modelling. 2015;39:23–24. S0307904X15001687. doi: 10.1016/j.apm.2015.03.016
  • Yang L, Deng ZC. An inverse backward problem for degenerate parabolic equations. Numer Meth for Partial Differ Equ. 2017;33:1900–1923. doi: 10.1002/num.22165

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