Geodesic
On the construction of the trajectory of a dynamical system with initial data on the hyperplanes
The Bulletin of Irkutsk State University. Series Mathematics, Tome 12 (2015), pp. 93-105 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we consider the problems of correct solvability of the initial value problem for a class of differential equations in Banach spaces. We apply the method of reduction of degenerate differential equation to the regular problems using the properties of the Jordan structure of the equation operator coefficients. The sufficient conditions for the correct solvability and stability as $ t \rightarrow +\infty$ of the initial value problem for the equations unsolved according to derivatives depending on the equation operator coefficients are obtained. The abstract theorems are used for statement and investigation of initial value problems for partial differential equation and integral equation. 
@article{IIGUM_2015_12_a8,
     author = {O. A. Romanova and N. A. Sidorov},
     title = {On the construction of the trajectory of a dynamical system with initial data on the hyperplanes},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {93--105},
     year = {2015},
     volume = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2015_12_a8/}
}
TY  - JOUR
AU  - O. A. Romanova
AU  - N. A. Sidorov
TI  - On the construction of the trajectory of a dynamical system with initial data on the hyperplanes
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2015
SP  - 93
EP  - 105
VL  - 12
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2015_12_a8/
LA  - ru
ID  - IIGUM_2015_12_a8
ER  - 
%0 Journal Article
%A O. A. Romanova
%A N. A. Sidorov
%T On the construction of the trajectory of a dynamical system with initial data on the hyperplanes
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2015
%P 93-105
%V 12
%U http://geodesic.mathdoc.fr/item/IIGUM_2015_12_a8/
%G ru
%F IIGUM_2015_12_a8
O. A. Romanova; N. A. Sidorov. On the construction of the trajectory of a dynamical system with initial data on the hyperplanes. The Bulletin of Irkutsk State University. Series Mathematics, Tome 12 (2015), pp. 93-105. http://geodesic.mathdoc.fr/item/IIGUM_2015_12_a8/

[1] Gantmacher F. R., The theory of matrices, Nauka, M., 1988, 552 pp. | MR

[2] Gilmutdinova A. F., “On nonuniqueness of solutions to the Showalter–Sidorov problem for the Plotnikov model”, Vestnik of Samara State University, 2007, no. 9/1(59), 85–90 (in Russian) | MR | Zbl

[3] Demidovich B. P., Lectures on mathematical stability theory, Lan', St. Petersburg, 2008, 480 pp.

[4] Zagrebina S. A., “On the problem Showalter–Sidorov”, Russian Mathematics [Izvestiya VUZ. Matematika], 2007, no. 3, 22–28 | MR | Zbl

[5] Zagrebina S. A., Sagadeeva M. A., “The generalized Showalter–Sidorov problem for Sobolev type equations with strong $(L,p)$-radial operator”, Vestnik of Magnitogorsk State University, Mathematics, 2006, no. 9, 17–27 (in Russian) | Zbl

[6] Keller A. V., “The algorithm for the numerical solution of the Showalter–Sidorov problem for the Leontiev systems”, Vestnik of South Ural State Univirsity, Computer technology, management, electronics, 2009, no. 26, 82–86

[7] Keller A. V., “Leontiev type systems: classes of problems with the initial condition Showalter–Sidorov and numerical solutions”, Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya “Matematika”, 2010, no. 3, 30–43 | Zbl

[8] Keller A. V., “The algorithm for solving of the Showalter–Sidorov problem for Leontiev models”, Vestnik of South Ural State Univirsity, Mat. modeling and programming, 2011, no. 7, 40–46 | Zbl

[9] Lavrentiev M. M., Saveliev L. Ja., Operator theory and ill-posed problems, IM SB RAS, Novosibirsk, 1999, 702 pp. | MR

[10] Loginov B. V., Sidorov N. A., “Group symmetry of the Lyapunov–Schmidt and iterative methods in the problem of a bifurcation point”, Matematicheskii Sbornik, 182:5 (1991), 681–691 | MR

[11] Romanova O. A., “On a class of differential equations with the derivatives of the functionals”, Approximate methods for solving operator equations and their applications, Irkutsk, 1982, 108–120 | MR | Zbl

[12] Sidorov D. N., The methods of analysis of integral dynamic models: theory and applications, Irkutsk State University, Irkutsk, 2013, 293 pp.

[13] Sidorov N. A., “On a class of degenerate differential equations with the convergence”, Mat. notes, 35:4 (1984), 569–578 | MR | Zbl

[14] Sidorov N. A., The general problems of regularization in the branching theory, ISU, Irkutsk, 1982, 312 pp. | MR

[15] Sidorov N. A., “The explicit and implicit parametrization in the construction of branching solutions by Iierative methods”, Matematicheskii Sbornik, 182:2 (1995), 129–141 | MR

[16] Sidorov N. A., Blagodatskaya E. B., “Differential equations with Fredholm Opretorom of the leading differential expression”, Doklady Akademii Nauk, 39:5 (1992)

[17] Sidorov N. A., Romanova O. A., Differential Equations, 19 (1983) | MR | Zbl

[18] Sidorov N. A., Romanova O. A., “Differential-difference equations with Fredholm operator in the main part”, Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya “Matematika”, 1 (2007), 254–266

[19] Trenogin V. A., Functional Analysis, Fizmatlit, M., 2002, 488 pp.

[20] Trenogin V. A., Filippov A. F. (eds.), Nonlinear analysis and nonlinear differential equations, Fizmatlit, M., 2003, 464 pp. | MR

[21] N. A. Sidorov, D. N. Sidorov, R. Yu. Leont'ev, “Successive approximations to the solutions to nonlinear equations with a vector parameter in a nonregular case”, Journal of Applied and Industrial Mathematics, 6:3 (2012), 387–392 | DOI | MR | Zbl

[22] N. A. Sidorov, R. Yu. Leont'ev, A. I. Dreglya, “On small solutions of nonlinear equations with vector parameter in sectorial neighborhoods”, Mathematical Notes, 91:1 (2012), 90–104 | DOI | MR | Zbl

[23] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev type equations and degenerate semigroups of operators, Inverse and ill-posed problems series, VSP, Utrecht–Boston–Köln–Tokyo, 2003 | MR | Zbl