Geodesic
Problems of Optimal and Hard Control over Solutions of Special Type of Nonstationary Sobolev Type Equations
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 135 (2014) no. 2, pp. 33-38 Cet article a éte moissonné depuis la source Math-Net.Ru

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Sobolev type equations now constitute a vast area of nonclassical equations of mathematical physics. Those called nonclassical equations of mathematical physics, whose representation in the form of equations or systems of equations partial does not fit within one of the classical types (elliptic, parabolic or hyperbolic). In this paper we prove the existence of a unique optimal and hard control over solutions of Showalter–Sidorov problem for nonstationary operator-differential equations unresolved with respect to the time derivative. In this case, one of the operators in the equation is multiplied by a scalar function of the time-variable, besades stationary equation has a strong continuous degenerate resolving semigroup of operators. Apart from the introduction and bibliography article comprises two parts. The first part provides the necessary information regarding the theory of $p$-radial operators, the second contains the proof of main results of this article.
Keywords: optimal control, hard control, nonstationary Sobolev type equations, relatively radial case. 
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M. A. Sagadeeva; A. N. Shulepov. Problems of Optimal and Hard Control over Solutions of Special Type of Nonstationary Sobolev Type Equations. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 135 (2014) no. 2, pp. 33-38. http://geodesic.mathdoc.fr/item/VSGTU_2014_135_2_a2/

[1] G. A. Sviridyuk, S. A. Zagrebina, “The Showalter–Sidorov problem as a phenomena of the Sobolev–type equations”, Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Ser. Matematika, 3:1 (2010), 104–125 (In Russian) | Zbl

[2] G. V. Demidenko, S. V. Uspenskiy, Uravneniya i sistemy, ne razreshennyye otnositel'no starshey proizvodnoy [Equations and systems that are not solved with respect to the highest derivative], Nauchnaya Kniga Publ., Novosibirsk, 1998, xviii+437 pp. | MR | Zbl

[3] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev type equations and degenerate semigroups of operators, Inverse and Ill-Posed Problems Series, VSP, Utrecht, Boston, 2003, viii+216 pp. | MR | Zbl

[4] A. B. Al'shin, M. O. Korpusov, A. G. Sveshnikov, Blow-up in nonlinear Sobolev type equations, De Gruyter Series in Nonlinear Analysis and Applications, 15, Walter de Gruyter Co., Berlin, 2011, xii+648 pp. | MR

[5] M. A. Sagadeyeva, A. N. Shulepov, “The Approximations for Degenerate $C_0$-semigroup”, Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming Computer Software, 6:2 (2013), 133–137 (In Russian) | Zbl

[6] M. A. Sagadeyeva, A. D. Badoyan, “The Optimal Control over Solutions of Special Form of Nonstacionary Sobolev Type Equations in Relatively Spectral Case”, Vestnik Magnitogorskogo Gosudarstvennogo Universiteta. Matematika, 2013, no. 15, 68–80 (In Russian)

[7] J. L. Lions, Control of distributed singular systems, Gauther-Villars, Paris, 1985, 552 pp.; John Wiley Sons Inc., New York, 1987, 576 pp.; Zh. L. Lions, Upravlenie singulyarnymi raspredelennymi sistemami, Nauka, M., 1987, 368 pp. | MR