Geodesic
Solution asymptotics in a~problem of optimal boundary control of a~flow through a~part of the boundary
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 116-127

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We consider a problem of optimal control through a part of the boundary of solutions to an elliptic equation in a bounded domain with smooth boundary with a small parameter at the Laplace operator and integral constraints on the control. A complete asymptotic expansion of the solution to this problems in powers of the small parameter is constructed.
Keywords: singular problems, optimal control, boundary value problems for systems of partial differential equations, asymptotic expansions. 
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     author = {A. R. Danilin},
     title = {Solution asymptotics in a~problem of optimal boundary control of a~flow through a~part of the boundary},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {116--127},
     publisher = {mathdoc},
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     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a10/}
}
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A. R. Danilin. Solution asymptotics in a~problem of optimal boundary control of a~flow through a~part of the boundary. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 116-127. http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a10/