Suboptimal boundary controls for elliptic equation in critically perforated domain
Ciro D'Apice, Umberto De Maio, Peter I. Kogut (2008)
Annales de l'I.H.P. Analyse non linéaire
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Ciro D'Apice, Umberto De Maio, Peter I. Kogut (2008)
Annales de l'I.H.P. Analyse non linéaire
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Saint Jean Paulin, J., Zoubairi, H. (2002)
Portugaliae Mathematica. Nova Série
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Conca, Carlos, Osses, Axel, Saint Jean Paulin, Jeannine (2001)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Peter I. Kogut, Günter Leugering (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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We are concerned with the asymptotic analysis of optimal control problems for -D partial differential equations defined on a periodic planar graph, as the period of the graph tends to zero. We focus on optimal control problems for elliptic equations with distributed and boundary controls. Using approaches of the theory of homogenization we show that the original problem on the periodic graph tends to a standard linear quadratic optimal control problem for a two-dimensional homogenized...
Yi, F., Shih, T.M., Yong, J. (1997)
Portugaliae Mathematica
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Hengyan Li, Shuguan Ji (2011)
Open Mathematics
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This paper is concerned with an optimal control problem governed by the nonlinear one dimensional periodic wave equation with x-dependent coefficients. The control of the system is realized via the outer function of the state. Such a model arises from the propagation of seismic waves in a nonisotropic medium. By investigating some important properties of the linear operator associated with the state equation, we obtain the existence and regularity of the weak solution to the state equation....
Wang, Jinrong, Xiang, X., Wei, W. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Carlos Conca, François Murat, Claudia Timofte (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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The limit behavior of the solutions of Signorini’s type-like problems in periodically perforated domains with period is studied. The main feature of this limit behaviour is the existence of a critical size of the perforations that separates different emerging phenomena as . In the critical case, it is shown that Signorini’s problem converges to a problem associated to a new operator which is the sum of a standard homogenized operator and an extra zero order term (“strange term”) coming...
Valadier, Michel (1997)
Portugaliae Mathematica
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