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Asymptotic Analysis of Optimal Control Problems on Periodic Singular Graphs

  • Peter I. Kogut
  • Günter R. Leugering
Part of the Systems & Control: Foundations & Applications book series (SCFA)

Abstract

Partial differential equations (PDEs) on graphs have frequently been considered in the literature, beginning with the works of Lumer (1980) and A. Vol’pert (1972). We also mention Lagnese, Leugering, and Schmidt (1994), Lagnese and Leugering (2004), Pokornyi et al. (2004), and von Below (1993).

Keywords

Optimal Control Problem Asymptotic Analysis Integral Identity Constrain Minimization Problem Suboptimal Control 
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References

  1. 163.
    J. E. Lagnese and G. Leugering. Domain Decomposition Methods in Optimal Control of Partial Differential Equations. Birkhäuser, Basel, 2004. MATHGoogle Scholar
  2. 164.
    J. E. Lagnese, G. Leugering, and E. J. P. G. Schmidt. Modelling, Analysis and Control of Multi-Link Flexible Structures. Birkhäuser, Basel, 1994. Google Scholar
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    G. Lumer. Connecting of local operators and evolution equations on networks. In Potential Theory, pages 219–234. Springer, New York, 1980. Google Scholar
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    Yu. V. Pokornyi, O. M. Penkin, V. I. Pryadiev, A. V. Borovskikh, K. P. Lazarev, and S. A. Shabrov. Differential Equations on Geometrical Graphs. Fizmatlit, Moskow, 2004. (in Russian) Google Scholar
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    A. I. Vol’pert. Differential equations on graphs. Math. Sbornik, 88(4):578–588, 1972. MathSciNetGoogle Scholar
  6. 248.
    J. von Below. Parabolic Network Equations. PhD thesis, Eberhard–Karis–Universität, Tübingen, 1993. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics and Mechanics, Department of Differential EquationsOles Honchar Dnipropetrovsk National UniversityDnipropetrovskUkraine
  2. 2.Department of Mathematics, Chair of Applied Mathematics IIFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany

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