Numerical studies of parameter estimation techniques for nonlinear evolution equations

Azmy S. Ackleh; Robert R. Ferdinand; Simeon Reich

Kybernetika (1998)

  • Volume: 34, Issue: 6, page [693]-712
  • ISSN: 0023-5954

Abstract

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We briefly discuss an abstract approximation framework and a convergence theory of parameter estimation for a general class of nonautonomous nonlinear evolution equations. A detailed discussion of the above theory has been given earlier by the authors in another paper. The application of this theory together with numerical results indicating the feasibility of this general least squares approach are presented in the context of quasilinear reaction diffusion equations.

How to cite

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Ackleh, Azmy S., Ferdinand, Robert R., and Reich, Simeon. "Numerical studies of parameter estimation techniques for nonlinear evolution equations." Kybernetika 34.6 (1998): [693]-712. <http://eudml.org/doc/33399>.

@article{Ackleh1998,
abstract = {We briefly discuss an abstract approximation framework and a convergence theory of parameter estimation for a general class of nonautonomous nonlinear evolution equations. A detailed discussion of the above theory has been given earlier by the authors in another paper. The application of this theory together with numerical results indicating the feasibility of this general least squares approach are presented in the context of quasilinear reaction diffusion equations.},
author = {Ackleh, Azmy S., Ferdinand, Robert R., Reich, Simeon},
journal = {Kybernetika},
keywords = {nonlinear evolution equation; parameter estimation; nonlinear evolution equation; parameter estimation},
language = {eng},
number = {6},
pages = {[693]-712},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Numerical studies of parameter estimation techniques for nonlinear evolution equations},
url = {http://eudml.org/doc/33399},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Ackleh, Azmy S.
AU - Ferdinand, Robert R.
AU - Reich, Simeon
TI - Numerical studies of parameter estimation techniques for nonlinear evolution equations
JO - Kybernetika
PY - 1998
PB - Institute of Information Theory and Automation AS CR
VL - 34
IS - 6
SP - [693]
EP - 712
AB - We briefly discuss an abstract approximation framework and a convergence theory of parameter estimation for a general class of nonautonomous nonlinear evolution equations. A detailed discussion of the above theory has been given earlier by the authors in another paper. The application of this theory together with numerical results indicating the feasibility of this general least squares approach are presented in the context of quasilinear reaction diffusion equations.
LA - eng
KW - nonlinear evolution equation; parameter estimation; nonlinear evolution equation; parameter estimation
UR - http://eudml.org/doc/33399
ER -

References

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  2. Ackleh A. S., Fitzpatrick B. G., Estimation of discontinuous parameters in general parabolic systems, Kybernetika 32 (1996), 543–556 (1996) MR1438104
  3. Ackleh A. S., Reich S., 10.1080/01630569808816867, Numer. Funct. Anal. Optim. 19 (1998), 933–947 (1998) Zbl0922.35185MR1656403DOI10.1080/01630569808816867
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  6. Banks H. T., Reich S., Rosen I. G., 10.1137/0328033, SIAM J. Control Optim. 28 (1990), 552–569 (1990) Zbl0722.47058MR1047423DOI10.1137/0328033
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  12. Fitzpatrick B. G., 10.1080/01630569508816650, Numer. Funct. Anal. Optim. 16 (1995), 847–866 (1995) Zbl0839.76081MR1355277DOI10.1080/01630569508816650
  13. Freeze R. A., Cherry J., Groundwater, Prentice–Hall, Englewood Cliffs, N. J. 1979 
  14. Johnson C., Numerical Solution of Partial Differential Equations by The Finite Element Method, Cambridge Univ. Press, Cambridge 1987 Zbl0628.65098MR0925005
  15. Kluge R., Langmach H., On some Problems of Determination of Functional Parameters in Partial Differential Equations, In: Distributed Parameter Systems: Modeling and Identification (Lecture Notes in Control and Information Sciences 1), Springer–Verlag, Berlin 1978, pp. 298–309 (1978) MR0513638
  16. Pao C. V., Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York 1992 Zbl0777.35001MR1212084
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