Voir la notice de l'article provenant de la source Math-Net.Ru
@article{CHFMJ_2017_2_1_a5, author = {M. V. Plekhanova}, title = {Solvability of control problems for degenerate evolution equations of fractional order}, journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal}, pages = {53--65}, publisher = {mathdoc}, volume = {2}, number = {1}, year = {2017}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_1_a5/} }
TY - JOUR AU - M. V. Plekhanova TI - Solvability of control problems for degenerate evolution equations of fractional order JO - Čelâbinskij fiziko-matematičeskij žurnal PY - 2017 SP - 53 EP - 65 VL - 2 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_1_a5/ LA - ru ID - CHFMJ_2017_2_1_a5 ER -
M. V. Plekhanova. Solvability of control problems for degenerate evolution equations of fractional order. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 1, pp. 53-65. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_1_a5/
[1] V. E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, New York, 2011, 450 pp. | MR
[2] V. V. Uchaykin, Fractional derivatives method, Artishok Publ., Ulyanovsk, 2008, 510 pp. (In Russ.)
[3] F. Mainardi, “The time fractional diffusion-wave equations”, Radiophysics and Quantum Electronics, 38 (1995), 13–24 | DOI | MR
[4] E. G. Bajlekova, Fractional Evolution Equations in Banach Spaces, PhD thesis, Eindhoven Univ. of Technology, Univ. Press Facilities, 2001, 107 pp. | MR | Zbl
[5] A. V. Pskhu, Partial differential equations of fractional order, Nauka Publ., Moscow, 2005, 199 pp. (In Russ.) | MR
[6] M. V. Plekhanova, A. F. Islamova, “Issledovanie linearizovannoi sistemy uravnenii Bussineska metodami teorii vyrozhdennykh polugrupp”, Vestn. Chelyab. gos. un-ta. Matematika. Mekhanika. Informatika, 20 (158):11 (2009), 62–69 (In Russ.) | MR
[7] V. E. Fedorov, D. M. Gordievskikh, M. V. Plekhanova, “quations in Banach spaces with a degenerate operator under a fractional derivative”, Differential equations, 51:10 (2015), 1360–1368 | DOI | DOI | MR | Zbl
[8] M. V. Plekhanova, “Strong solutions of quasilinear equations in Banach spaces not solvable with respect to the highest-order derivative”, Discrete and Continuous Dynamical systems. Series S, 9:3 (2016), 833–847 | DOI | MR
[9] M. V. Plekhanova, “Nonlinear equations with degenerate operator at fractional Caputo derivative”, Mathematical methods in the applied sciences | DOI
[10] V. E. Fedorov, M. V. Plekhanova, “Weak solutions and the quadratic regulator problem for a degenerate differential equation in Hilbert space”, Computational technologies, 9:2 (2004), 92–102 (In Russ.) | MR | Zbl
[11] M. V. Plekhanova, V. E. Fedorov, “Zadacha optimalnogo upravleniya dlya odnogo klassa vyrozhdennykh uravnenii”, Izv. RAN. Teoriya i sistemy upr., 2004, no. 5, 40–44 | MR
[12] M. V. Plekhanova, V. E. Fedorov, “An optimality criterion in a control problem for a Sobolev-type linear equation”, Journal of Computer and System Sciences International, 46:2 (2007), 248–254 | DOI | MR | Zbl
[13] M. V. Plekhanova, “Mixed control problem for the linearized quasi-stationary phase field system of equations”, Materials Science Forum, 845 (2016), 170–173 | DOI
[14] M. V. Plekhanova, “Strong solutions of a nonlinear degenerate evolution equation of fractional order”, Siberian Journal of Pure and Applied Mathematics, 16:3 (2016), 61–74 (In Russ.) | MR
[15] A. V. Fursikov, Optimal control for distributed systems. Theory and applications, Nauchnaya Kniga Publ., Novosibirsk, 1999, 350 pp. (In Russ.)
[16] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science Publ., Amsterdam–Boston–Heidelberg, 2006, 541 pp. | MR | Zbl
[17] A. N. Gerasimov, “Generalization of linear deformation laws and their application to internal friction problems”, Applied mathematics and mechanics, 12 (1948), 529–539 (In Russ.) | MR
[18] M. Caputo, “Linear model of dissipation whose $Q$ is almost frequency independent”, Geophysical J. of the Royal Astronomical Soc., 13 (1967), 383–393 | DOI | MR
[19] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, VSP, Utrecht–Boston, 2003, vii+216 pp. | MR | Zbl
[20] J.-L. Lions, Quelques Méthodes De Résolution Des Problémes Aux Limites Non-Linéaires, Dunod Gauthier-Villars, Paris, 1969, xx+554 pp. (In Russ.) | MR | MR
[21] M.O. Korpusov , A.G. Sveshnikov, Nonlinear functional analysis and mathematical modeling in physics: Geometric and topological properties of linear spaces, Krasand Publ., Moscow, 2011, 416 pp. (In Russ.)
[22] A.P. Oskolkov, “To the stability theory for solutions of the semilinear dissipative Sobolev type equations”, Notes of scientific seminars of POMI RAS, 200, 1992, 139–148 (In Russ.)