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Distributed Control with the General Quadratic Criterion in a Special Norm for Systems Described by Parabolic–Hyperbolic Equations with Nonlocal Boundary Conditions

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Abstract

We obtain conditions to find the distributed optimal control for parabolic-hyperbolic equations with nonlocal boundary conditions and general quadratic criterion in the special norm. The unique solvability of systems for finding the optimal solution is established, systems’ kernels are estimated, and the convergence of solutions of the problem is proved.

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References

  1. A. Ashyralyev and A. Yurtsever, “On a nonlocal boundary value problem for semilinear hyperbolic-parabolic equations,” Nonlinear Analysis: Theory, Methods&Applications, 47, No. 5, 3585–3592 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  2. L. Stupyalis, “A boundary-value problem for the stationary system of equations of magnetohydrodynamics. Boundary-value problems of mathematical physics,” Tr. MIAN SSSR, 147, No. 10, 169–193 (1980).

    MATH  Google Scholar 

  3. V. O. Kapustyan and I. O. Pyshnograiev, “The existence and uniqueness conditions for the solution of the parabolic–hyperbolic equation with nonlocal boundary conditions,” Naukovi Visti NTUU KPI, No. 4, 72–86 (2012).

  4. A. I. Egorov, Optimal Control of Linear Systems [in Russian], Naukova Dumka, Kyiv (1988).

    Google Scholar 

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Authors and Affiliations

  1. National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kyiv, Ukraine

    V. O. Kapustyan & I. O. Pyshnograiev

Authors
  1. V. O. Kapustyan
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  2. I. O. Pyshnograiev
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Correspondence to V. O. Kapustyan.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 3, May–June, 2015, pp. 132–142.

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Kapustyan, V.O., Pyshnograiev, I.O. Distributed Control with the General Quadratic Criterion in a Special Norm for Systems Described by Parabolic–Hyperbolic Equations with Nonlocal Boundary Conditions. Cybern Syst Anal 51, 438–447 (2015). https://doi.org/10.1007/s10559-015-9735-8

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  • DOI: https://doi.org/10.1007/s10559-015-9735-8

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