Geodesic
Optimal Control in Higher-Order Sobolev-Type Mathematical Models with $(A,p)$-Bounded Operators
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 7 (2014) no. 2, pp. 129-135

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This article deals with the optimal control problem for an incomplete Sobolev-type equation of high order. We prove an existence and uniqueness theorem for strong solutions to the initial value problem for a given equation. We obtain sufficient and necessary conditions for the existence and uniqueness of optimal control of these solutions. We use the ideas and methods developed by G. A. Sviridyuk and his school. The proof of the existence and uniqueness of optimal control rests on the theory of optimal control developed by J.-L. Lions.
Keywords: Sobolev-type equations; strong solutions; optimal control. 
@article{VYURU_2014_7_2_a12,
     author = {O. N. Tsyplenkova},
     title = {Optimal {Control} in {Higher-Order} {Sobolev-Type} {Mathematical} {Models} with $(A,p)${-Bounded} {Operators}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {129--135},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2014_7_2_a12/}
}
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O. N. Tsyplenkova. Optimal Control in Higher-Order Sobolev-Type Mathematical Models with $(A,p)$-Bounded Operators. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 7 (2014) no. 2, pp. 129-135. http://geodesic.mathdoc.fr/item/VYURU_2014_7_2_a12/