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Optimality Conditions of a Three-Dimension Non-smooth Thermodynamic System of Sea Ice

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Complex Sciences (Complex 2009)

Abstract

This study is intended to provide the mathematical foundation for the numerical computation of the parameter identification problems of the three-dimensional two-layer thermodynamic system of sea ice. The non-smooth thermodynamic system with mixed boundary conditions is established, its properties are obtained and the first-order necessary conditions of the parameter identification problem of the non-smooth system are derived.

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References

  1. Haskell, T.: What’s so important about sea ice? Water & Atmosphere 11(3), 28–29 (2003)

    Google Scholar 

  2. Wolff, E.: Whither Antarctic sea ice? Science 302, 1164 (2003)

    Google Scholar 

  3. Laxon, S., Peacock, N., Smith, D.: High interannual variability of sea ice thickness in the Arctic region. Nature 425, 947–950 (2003)

    Article  Google Scholar 

  4. Maykut, G.A., Untersteiner, N.: Some results from a time-dependent thermodynamic model of sea ice. J. Geophys. Res. 76, 1550–1575 (1971)

    Article  Google Scholar 

  5. Gabison, R.: A thermodynamic model of the formation growth and decay of first-year sea ice. J. Glaciol. 33, 105–109 (1987)

    Google Scholar 

  6. Ebert, E.E., Curry, J.A.: An intermediate one-dimensional thermodynamic sea-ice model for investigating ice-atmosphere interaction. J. Geophys. Res. 98(C6), 10085–10109 (1993)

    Article  Google Scholar 

  7. Cheng, B.: On the numerical resolution in a thermodynamic sea-ice model. J. Glaciol. 48(161), 301–311 (2002)

    Article  Google Scholar 

  8. Reid, T., Crout, N.: A thermodynamic model of freshwater Antarctic lake ice. Ecol. Model. 210, 231–241 (2008)

    Article  Google Scholar 

  9. Shidfar, A., Karamali, G.R.: Numerical solution of inverse heat conduction problem with nonstationary measurements. Appl. Math. Comput. 168(1), 540–548 (2005)

    MathSciNet  MATH  Google Scholar 

  10. Li, G.S.: Data compatibility and conditional stability for an inverse source problem in the heat equation. Appl. Math. Comput. 173, 566–581 (2006)

    MathSciNet  MATH  Google Scholar 

  11. Shidfar, A., Karamali, G.R., Damirchi, J.: An inverse heat conduction problem with a nonliear source term. Nonlinear Anal. 65, 615–621 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ikehata, M.: An inverse source problem for the heat equation and the enclosure method. Inverse Probl. 23, 183–202 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Christov, C.I., Marinov, T.: Identification of heat-conduction coefficient via method of variational imbedding. Math. Comput. Modell. 27(3), 109–116 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  14. Engl, H.W., Zou, J.: A new approach to convergence rate analysis of Tikhonov regularization for parameter identification in heat conduction. Inverse Probl. 16, 1907–1923 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Telejko, T., Malinowski, A.: Application of an inverse solution to the thermal conductivity identification using the finite element method. J. Mater. Process. Technol. 146, 145–155 (2004)

    Article  Google Scholar 

  16. Lv, W., Feng, E., Li, Z.: A coupled thermodynamic system of sea ice and its parameter identification. Appl. Math. Modell. 32, 1198–1207 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Lv, W., Feng, E., Lei, R.: Parameter Identification for a Nonlinear Thermodynamic System of Sea Ice. International Journal of Thermal Sciences 48, 195–203 (2009)

    Article  Google Scholar 

  18. Wang, Y.: L 2 Theories on Patial Differential Equation. Beijing University Press, Beijing (1989)

    Google Scholar 

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© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering

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Lv, W., Bao, H., Feng, E. (2009). Optimality Conditions of a Three-Dimension Non-smooth Thermodynamic System of Sea Ice. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02466-5_4

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  • DOI: https://doi.org/10.1007/978-3-642-02466-5_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02465-8

  • Online ISBN: 978-3-642-02466-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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