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On the asymptotic behavior of solutions to inverse problems for parabolic equations

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References

  1. A. N. Tikhonov and V. Ya. Arsenin, Methods for Solving Ill-Posed Problems [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  2. M. M. Lavrent'ev, V. G. Romanov and S. P. Shishatskiî, Ill-Posed Problems of Mathematical Physics and Analysis [in Russian], Nauka, Moscow (1980).

    MATH  Google Scholar 

  3. Yu. E. Anikonov, Some Methods for Studying Multidimensional Inverse Problems of Differential Equations [in Russian], Nauka, Novosibirsk (1978).

    Google Scholar 

  4. A. L. Bukhgeîm, Volterra Equations and Inverse Problems [in Russian], Nauka, Novosibirsk (1983).

    Google Scholar 

  5. A. M. Denisov, Introduction to the Theory of Inverse Problems [in Russian], Moscow Univ., Moscow (1994).

    Google Scholar 

  6. A. I. Prilepko and D. G. Orlovskiî, “On determining a parameter of an evolution equation and inverse problems of mathematical physics. II,” Differentsial'nye Uravneniya,21, No. 4, 694–700 (1985).

    Google Scholar 

  7. J. R. Cannon and Y. Lin, “Determination of a parameterp(t) in some quasilinear parabolic differential equations,” Inverse Problems,4, No. 1, 35–45 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  8. A. B. Kostin, “An inverse problem for the heat equation with integral overdetermination,” in: Inverse Problems for Mathematical Modeling of Physical Processes [in Russian], MIFI, Moscow, 1991, pp. 45–49.

    Google Scholar 

  9. V. L. Kamynin, “On passage to the limit in control problems with weakly converging coefficients,” Uspekhi Mat. Nauk,49, No. 4, 113–114 (1994).

    Google Scholar 

  10. V. L. Kamynin, “On convergence of the solutions of inverse problems for parabolic equations with weakly converging coefficients,” in: Elliptic and Parabolic Problems (Pont-a-Mousson, 1994), London Group Limited, London, 1995, pp. 130–151. (Pitman Res. Notes Math. Ser.;325.)

    Google Scholar 

  11. A. Friedman, “Asymptotic behavior of solutions of parabolic equations,” J. Math. Mech.,8, 372–392 (1959).

    Google Scholar 

  12. J.-L. Lions, Equations Differentielles Operationelles et Problemes aux Limits, Springer, Berlin (1961).

    Google Scholar 

  13. D. G. Aronson, “On the Green's function for second order parabolic differential equations with discontinuous coefficients,” Bull. Amer. Math. Soc.,69, 841–847 (1963).

    Article  MATH  MathSciNet  Google Scholar 

  14. T. I. Zelenyak, “On stabilization of solutions of boundary value problems for a second-order parabolic equation in a single space variable,” Differentsial'nye Uravneniya,4, No. 1, 34–45 (1968).

    MATH  Google Scholar 

  15. K.-O. Widman, “Asymptotic behavior of solutions of parabolic equations with discontinuous coefficients,” Math. Scand.,27, 113–131 (1970).

    MATH  MathSciNet  Google Scholar 

  16. J. Simon, “Quelques propriétés de solutions d'équations et d'inéquations d'évolution paraboliques non linéaires,” Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4),2, No. 4, 585–610 (1975).

    MATH  MathSciNet  Google Scholar 

  17. A. Arosio, “Asymptotic behavior ast→+∞ of solutions of linear parabolic equations with discontinuous coefficients in a bounded domain,” Comm. Partial Differential Equations,4, No. 7, 769–794 (1979).

    Article  MATH  MathSciNet  Google Scholar 

  18. V. L. Kamynin, “Asymptotic behavior of solutions to quasilinear parabolic equations in a bounded domain,” Sibirsk. Mat. Zh.,35, No. 2, 340–358 (1994).

    MathSciNet  Google Scholar 

  19. A. M. Il'in, A. C. Kalashnikov, and O. A. Oleînik, “Second-order linear equations of parabolic type,” Uspekhi Mat. Nauk,17, No. 3, 3–146 (1962).

    Google Scholar 

  20. T. I. Zelenyak and V. P. Mikhaîlov, “The asymptotic behavior ast→∞ of solutions to some boundary value problems of mathematical physics,” in: Partial Differential Equations (Proceedings of the Symposium Dedicated to Academician S. L. Sobolev on His Sixtieth Birthday) [in Russian], Nauka, Moscow, 1970, pp. 96–119.

    Google Scholar 

  21. A. K. Gushchin, V. P. Mikhaîlov, and L. A. Muraveî, “On stabilization of solutions to nonstationary boundary value problems for linear partial differential equations,” Dinamika Sploshn. Sredy (Novosibirsk),23, 57–91 (1975).

    Google Scholar 

  22. R. Riganti and E. Savateev, “Solution of an inverse problem for the nonlinear heat equation,” Comm. Partial Differential Equations,19, No. 9-10, 1611–1628 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  23. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  24. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order [Russian translation], Nauka, Moscow (1989).

    MATH  Google Scholar 

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Authors
  1. I. A. Vasin
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  2. V. L. Kamynin
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Additional information

The research was financially supported by the Russian Foundation for Basic Research (Grants 94-01-00289 and 96-01-00732).

Moscow. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 38, No. 4, pp. 750–766, July–August, 1997.

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Vasin, I.A., Kamynin, V.L. On the asymptotic behavior of solutions to inverse problems for parabolic equations. Sib Math J 38, 647–662 (1997). https://doi.org/10.1007/BF02674572

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  • DOI: https://doi.org/10.1007/BF02674572

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