Geodesic
Strongly continuous operator semigroups. Alternative approach
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 2, pp. 40-48 Cet article a éte moissonné depuis la source Math-Net.Ru

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Inheriting and continuing the tradition, dating back to the Hill–Iosida–Feller–Phillips–Miyadera theorem, the new way of construction of the approximations for strongly continuous operator semigroups with kernels is suggested in this paper in the framework of the Sobolev type equations theory, which experiences an epoch of blossoming. We introduce the concept of relatively radial operator, containing condition in the form of estimates for the derivatives of the relative resolvent, the existence of $C_0$-semigroup on some subspace of the original space is shown, the sufficient conditions of its coincidence with the whole space are given. The results are very useful in numerical study of different nonclassical mathematical models considered in the framework of the theory of the first order Sobolev type equations, and also to spread the ideas and methods to the higher order Sobolev type equations.
Keywords: strongly continuous semigroups of operators with kernals, approximations of semigroups.
Mots-clés : Sobolev type equation 
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A. A. Zamyshlyaeva. Strongly continuous operator semigroups. Alternative approach. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 2, pp. 40-48. http://geodesic.mathdoc.fr/item/VYURU_2013_6_2_a2/

[1] Hille E., Phillips R. S., Functional Analysis and Semi-Groups, American Mathematical Society, Providence, Rhode Island, 1957 ; E. Khille, R. Fillips, Funktsionalnyi analiz i polugruppy, IL, M., 1962 | MR | Zbl

[2] Sviridyuk G. A., Fedorov V. E., Linear Sobolev Type Equations and Degenerate Semigroups of Operators, VSP, Utrecht–Boston–Köln–Tokyo, 2003 | MR | Zbl

[3] Demidenko G. V., Uspenskii S. V., Partial Differential Equations and Systems Not Solvable with Respect to the Highest Order Derivative, Marcel Dekker, Inc., N. Y.–Basel–Hong Kong, 2003 | MR | Zbl

[4] Favini A., Yagi A., Degenerate Differential Equations in Banach Spaces, Marcel Dekker, Inc., N. Y.–Basel–Hong Kong, 1999 | MR | Zbl

[5] Sidorov N., Loginov B., Sinithyn A., Falaleev M., Lyapunov–Shmidt Methods in Nonlinear Analysis and Applications, Kluwer Academic Publishers, Dordrecht–Boston–London, 2002 | MR | Zbl

[6] Al'shin A. B., Korpusov M. O., Sveshnikov A. G., Blow-up in Nonlinear Sobolev Type Equations, Series in Nonlinear Analisys and Applications, 15, De Gruyter, 2011 | MR | Zbl

[7] Sviridyuk G. A., “Linear Sobolev Type Equations and Strongly Continuous Semigroups of the Resolving Operators with Kernels”, Doklady akademii nauk, 337:5 (1994), 581–584 | MR | Zbl

[8] Sviridyuk G. A., Zamyshlyaeva A. A., “The Phase Spaces of a Class of Linear Higher-order Sobolev Type Equations”, Differential Equations, 42:2 (2006), 269–278 | DOI | MR | Zbl