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A truncated spectral regularization method for a source identification problem

  • Ajoy Jana
  • M. Thamban Nair
Proceedings: ICMAA 2016
  • 33 Downloads

Abstract

Abstract inverse source problem of identifying the source function f in the abstract Cauchy problem \(u_t+Au=f(t),\, 0<t<\tau \) with \(u(0)=\phi _0\) when the data, the final value, \(u(\tau )=\phi _\tau \) is noisy is considered, where A is a densly defined self-adjont coercive unbounded operator on a Hilbert space H. This problem is known to be an ill-posed problem. A truncated spectral representation of a mild solution of the above problem is shown to be a regularized approximation, and error analysis is carried out when \(\phi _\tau \) is noisy as well as exact, and stability estimate is given under appropriate parameter choice strategies.

Keywords

Parabolic equations Semigroups Ill-posed problems Regularization 

Mathematics Subject Classification

35K90 47D06 47A52 65F22 

Notes

Acknowledgements

Ajoy Jana acknowledges the support received from the University Grant Commission, Government of India, for financial support. Sanction no is Sr. No. F.2-12/2002(SA-I), Ref No: Acad./R3/J.Rpt/2014.

References

  1. 1.
    Hasanov, A., and M. Slodicka. 2013. An analysis of inverse source problems with final time measured output data for heat conduction equation: a semigroup approch. Applied Mathematics Letters 26: 207–214.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Jana, A., and M.T. Nair. 2016. Truncated spectral regularization for an ill-posed non-homogeneous parabolic problem. Journal of Mathematical Analysis and Applications 438: 351–372.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Pazy, A. 1983. Semigroups of linear operators and application to partial differential equations. New York: Springer.CrossRefzbMATHGoogle Scholar
  4. 4.
    Yosida, K. 1980. Functional analysis. Heidelberg: Springer.zbMATHGoogle Scholar

Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  1. 1.Department of MathematicsI.I.T. MadrasChennaiIndia

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