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Variational method for the solution of problems of transmission with the principal conjugation condition

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Abstract

We prove the existence of a solution of a variational minimax problem that is equivalent to the problem of transmission. We propose an algorithm for the construction of approximate solutions and prove its convergence.

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References

  1. V. A. Il'in and I. A. Shishmarev, “Method of potentials for the Dirichlet and Neumann problems for equations with discontinuous coefficients,”Sib. Mat. Zh.,2, No. 1, 46–58 (1961).

    MATH  Google Scholar 

  2. M. Schechter, “A generalization of the problem of transmission,”Ann. Soc. Norm. Supér. Pisa,14, 207–236 (1960).

    MATH  MathSciNet  Google Scholar 

  3. Z. G. Sheftel', “Energetic inequalities and general boundary-value problems for elliptic equations with discontinuous coefficients,”Sib. Mat. Zh.,6, No. 3, 636–668 (1965).

    Google Scholar 

  4. B. Ya. Roitberg and Ya. A. Roitberg, “Elliptic boundary-value problems in nonsmooth domains,”Ukr. Mat. Zh.,47, No. 5, 701–709 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  5. B. Ya. Roitberg, “Problems of transmission in domains with nonsmooth boundaries,”Dop. Akad. Nauk Ukr., No. 3, 15–20 (1996).

    MathSciNet  Google Scholar 

  6. J.-L. Lions and E. Magenes,Problèmes aux Limites Non Homogénes et Applications, Dunod, Paris (1968).

    MATH  Google Scholar 

  7. I. V. Sergienko, V. V. Skopetskii, and V. S. Deineka,Mathematical Simulation and Investigation of Processes in Inhomogeneous Media [in Russian], Naukova Dumka, Kiev (1991).

    Google Scholar 

  8. I. Ekeland and R. Temam,Analyse Convexe et Problèmes Variationnels, Dunod, Paris (1974).

    MATH  Google Scholar 

  9. R. T. Rockafellar,Convex Analysis [Russian translation] Mir, Moscow (1973).

    MATH  Google Scholar 

  10. I. A. Lukovskii, M. Ya. Barnyak, and A. N. Komarenko,Approximate Methods for Solution of Problems in the Dynamics of Limited Volume of Liquid [in Russian], Naukova Dumka, Kiev (1984).

    Google Scholar 

  11. S. F. Feshchenko, I. A. Lukovskii, B. I. Rabinovich, and L. V. Dokuchaev,Methods for Locating Attached Masses of Liquids in Moving Cavities [in Russian], Naukova Dumka, Kiev (1969).

    Google Scholar 

  12. A. N. Komarenko and V. A. Trotsenko, “On the variational methods for solution of problems of oscillation of liquid in cavities of complex geometry”, in:Numerical-Analytic Methods for Investigation of Dynamics and Stability of Multidimensional Systems [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1985), pp. 66–74.

    Google Scholar 

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Authors
  1. O. N. Komarenko
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  2. V. A. Trotsenko
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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 762–775, June, 1999.

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Komarenko, O.N., Trotsenko, V.A. Variational method for the solution of problems of transmission with the principal conjugation condition. Ukr Math J 51, 847–863 (1999). https://doi.org/10.1007/BF02591973

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  • DOI: https://doi.org/10.1007/BF02591973

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