Geodesic
On the unique solvability of nonlocal problems with integral conditions for a hybrid system of partial differential equations
Eurasian mathematical journal, Tome 9 (2018) no. 3, pp. 14-24.

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A nonlocal problem with integral conditions for a hybrid system of partial differential equations is investigated. Based on the results for nonlocal problems for a system of hyperbolic equations coefficient conditions are established ensuring the existence of classical solutions to a nonlocal problem with integral conditions for a hybrid system of partial differential equations, and algorithms of finding such solutions are suggested. 
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A. T. Assanova; A. P. Sabalakhova. On the unique solvability of nonlocal problems with integral conditions for a hybrid system of partial differential equations. Eurasian mathematical journal, Tome 9 (2018) no. 3, pp. 14-24. http://geodesic.mathdoc.fr/item/EMJ_2018_9_3_a1/

[1] A.T. Asanova, D.S. Dzhumabaev, “Unique solvability of the boundary value problem for systems of hyperbolic equations with data on the characteristics”, Computational Mathematics and Mathematical Physics, 42:11 (2002), 1609–1621 | MR | Zbl

[2] A.T. Asanova, D.S. Dzhumabaev, “Unique solvability of nonlocal boundary value problems for systems of hyperbolic equations”, Differential Equations, 39:10 (2003), 1414–1427 | DOI | MR | Zbl

[3] A.T. Asanova, D.S. Dzhumabaev, “Criteria of well-posed solvability of boundary value problem for system of hyperbolic equations”, Izvestia NAN Respubl. Kazakhstan. Ser. phyz.-mathem., 2002, no. 3, 20–26 (in Russian) | MR

[4] A.T. Asanova, D.S. Dzhumabaev, “Correct solvability of a nonlocal boundary value problem for systems of hyperbolic equations”, Doklady Mathematics, 68:1 (2003), 46–49 | MR

[5] A.T. Asanova, D.S. Dzhumabaev, “Well-posed solvability of nonlocal boundary value problems for systems of hyperbolic equations”, Differential Equations, 41:3 (2005), 352–363 | DOI | MR | Zbl

[6] A.T. Asanova, “A Nonlocal boundary value problem for systems of quasilinear hyperbolic equations”, Doklady Mathematics, 74:3 (2006), 787–791 | DOI | MR

[7] A.T. Asanova, “On the unique solvability of a family of two-point boundary-value problems for systems of ordinary differential equations”, Journal of Mathematical Sciences, 150:5 (2008), 2302–2316 | DOI | MR | Zbl

[8] D.S. Dzhumabaev, A.T. Asanova, “Well-posed solvability of a linear nonlocal boundary value problem for systems of hyperbolic equations”, Dopovidi NAN Ukraine, 2010, no. 4, 7–11 (in Russian) | MR | Zbl

[9] A.T. Asanova, D.S. Dzhumabaev, “Well-posedness of nonlocal boundary value problems with integral condition for the system of hyperbolic equations”, Journal of Mathematical Analysis and Applications, 402:1 (2013), 167–178 | DOI | MR | Zbl

[10] D.S. Dzhumabaev, “Conditions the unique solvability of a linear boundary value problem for a ordinary differential equations”, USSR Computational Mathematics and Mathematical Physics, 29:1 (1989), 34–46 | DOI | MR | Zbl

[11] R. Goebel, R.G. Sanfelice, A.R. Teel, Hybrid dynamical systems, Princeton University Press, Princeton, 2012 | MR | Zbl

[12] N.D. Golubeva, L.S. Pul'kina, “A nonlocal problem with integral conditions”, Mathematical Notes, 59:3 (1996), 326–328 | DOI | MR | Zbl

[13] T.I. Kiguradze, Some boundary value problems for systems of linear partial differential equations of hyperbolic type, Mem. Differential Equations Math. Phys., 1, 1994, 144 pp. | MR | Zbl

[14] A.B. Kurzhanskii, P.A. Tochilin, “Weakly invariant sets of hybrid systems”, Differential Equations, 44:11 (2008), 1585–1594 | DOI | MR | Zbl

[15] R. Margellos, J. Lygeros, “Viable set computation for hybrid systems”, Nonlinear Analysis: Hybrid Systems, 10:1 (2013), 45–52 | DOI | MR

[16] A.M. Nakhushev, Problems with shift for a partial differential equations, Nauka, M., 2006 (in Russian) | MR

[17] B.I. Ptashnyck, Ill-posed boundary value problems for partial differential equations, Naukova Dumka, Kiev, 1984 (in Russian) | MR

[18] E. Santis, M.D. Benedetto, G. Pola, “Digital idle speed control of automotive engines a safety problem for hybrid systems”, Nonlinear Analysis, 65:9 (2006), 1705–1724 | DOI | MR | Zbl

[19] Yu.B. Senichenkov, Numerical modeling of hybrid systems, Izd-vo Politechn. un-ta, Saint-Petersburg, 2004 (in Russian)

[20] B.P. Tkach, L.B. Urmancheva, “Numerical-analytical method for finding solutions of systems with distributed parameters and integral condition”, Nonlinear Oscillations, 12:1 (2009), 110–119 | DOI | MR | Zbl

[21] A. Van der Schaft, H. Schumacher, An Introduction to hybrid dynamical systems, Lecture Notes in Control and Information Sciences, 251, Berlin, 2000 | MR | Zbl

[22] L. Yao, J. Li, “Stability and stabilization of a class of nonlinear impulsive hybrid systems based on FSM with MDADT”, Nonlinear Analysis: Hybrid Systems, 15:1 (2015), 1–10 | DOI | MR | Zbl

[23] C. Yuan, F. Wu, “Analysis and synthesis of linear impulsive hybrid systems with state-triggered jumps”, Nonlinear Analysis: Hybrid Systems, 14:1 (2014), 47–60 | DOI | MR | Zbl

[24] S.V. Zhestkov, “The Goursat problem with integral boundary conditions”, Ukranian Mathematical Journal, 42:1 (1990), 119–122 | DOI | MR | Zbl

[25] A.L. Zuyev, “Partial asymptotic stabilization of nonlinear distributed parameter systems”, Automatica, 41:1 (2005), 1–10 | MR | Zbl