Asymptotic behavior of impulsive parabolic problem with infinite-dimensional impulsive set

References

[1] M. Akhmet, Principles of Discontinuous Dynamical Systems, Springer, New York, 2010. 10.1007/978-1-4419-6581-3Search in Google Scholar

[2] J. M. Ball, Strongly continuous semigroups, weak solutions, and the variation of constants formula, Proc. Amer. Math. Soc. 63 (1977), no. 2, 370–373. 10.1090/S0002-9939-1977-0442748-6Search in Google Scholar

[3] E. M. Bonotto, M. C. Bortolan, A. N. Carvalho and R. Czaja, Global attractors for impulsive dynamical systems—a precompact approach, J. Differential Equations 259 (2015), no. 7, 2602–2625. 10.1016/j.jde.2015.03.033Search in Google Scholar

[4] E. M. Bonotto and M. Federson, Limit sets and the Poincaré–Bendixson theorem in impulsive semidynamical systems, J. Differential Equations 244 (2008), no. 9, 2334–2349. 10.1016/j.jde.2008.02.007Search in Google Scholar

[5] E. M. Bonotto and P. Kalita, On attractors of generalized semiflows with impulses, J. Geom. Anal. 30 (2020), no. 2, 1412–1449. 10.1007/s12220-019-00143-0Search in Google Scholar

[6] T. Caraballo and J. M. Uzal, Dynamics of nonautomous impulsive multivalued processes, Set-Valued Var. Anal. 31 (2023), no. 1, Paper No. 7. 10.1007/s11228-023-00667-2Search in Google Scholar

[7] K. Ciesielski, On stability in impulsive dynamical systems, Bull. Pol. Acad. Sci. Math. 52 (2004), no. 1, 81–91. 10.4064/ba52-1-9Search in Google Scholar

[8] S. Dashkovskiy and P. Feketa, Input-to-state stability of impulsive systems and their networks, Nonlinear Anal. Hybrid Syst. 26 (2017), 190–200. 10.1016/j.nahs.2017.06.004Search in Google Scholar

[9] S. Dashkovskiy and P. Feketa, Asymptotic properties of Zeno solutions, Nonlinear Anal. Hybrid Syst. 30 (2018), 256–265. 10.1016/j.nahs.2018.06.005Search in Google Scholar

[10] S. Dashkovskiy, O. Kapustyan and Y. Perestyuk, Stability of uniform attractors of impulsive multi-valued semiflows, Nonlinear Anal. Hybrid Syst. 40 (2021), Paper No. 101025. 10.1016/j.nahs.2021.101025Search in Google Scholar

[11] S. Dashkovskiy, O. Kapustyan and I. Romaniuk, Global attractors of impulsive parabolic inclusions, Discrete Contin. Dyn. Syst. Ser. B 22 (2017), no. 5, 1875–1886. 10.3934/dcdsb.2017111Search in Google Scholar

[12] S. Dashkovskiy and M. Kosmykov, Input-to-state stability of interconnected hybrid systems, Automatica J. IFAC 49 (2013), no. 4, 1068–1074. 10.1016/j.automatica.2013.01.045Search in Google Scholar

[13] S. Dashkovskiy and A. Mironchenko, Input-to-state stability of nonlinear impulsive systems, SIAM J. Control Optim. 51 (2013), no. 3, 1962–1987. 10.1137/120881993Search in Google Scholar

[14] P. Feketa and Y. Perestyuk, Perturbation theorems for a multifrequency system with impulses, Nelīnīĭnī Koliv. 18 (2015), no. 2, 280–289; translation in J. Math. Sci. (N.Y.) 217 (2016), no. 4, 515–524. Search in Google Scholar

[15] O. Kapustyan, O. Kapustian, I. Korol and B. Rubino, Uniform attractor of impulse-perturbed reaction-diffusion system, Math. Mech. Complex Syst. 11 (2023), no. 1, 45–55. 10.2140/memocs.2023.11.45Search in Google Scholar

[16] O. V. Kapustyan and M. O. Perestyuk, Global attractors of impulsive infinite-dimensional systems (in Ukrainian), Ukraïn. Mat. Zh. 68 (2016), no. 4, 517–528; translation in Ukrainian Math. J. 68 (2016), no. 4, 583–597. Search in Google Scholar

[17] O. V. Kapustyan, M. O. Perestyuk and I. V. Romanyuk, Stability of the global attractors of impulsive infinite-dimensional systems (in Ukrainian), Ukraïn. Mat. Zh. 70 (2018), no. 1, 29–39; translation in Ukrainian Math. J. 70 (2018), no. 1, 30–41. Search in Google Scholar

[18] A. G. Nakonechnyi, E. A. Kapustian and A. A. Chikrii, Control of impulse systems in conflict situations, J. Automat. Inform. Sci. 51 (2019), no. 9, 1–11. 10.1615/JAutomatInfScien.v51.i9.10Search in Google Scholar

[19] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, New York, 1983. 10.1007/978-1-4612-5561-1Search in Google Scholar

[20] M. Perestyuk and O. Kapustyan, Long-time behavior of evolution inclusion with non-damped impulsive effects, Mem. Differ. Equ. Math. Phys. 56 (2012), 89–113. Search in Google Scholar

[21] J. C. Robinson, Infinite-Dimensional Dynamical Systems, Cambridge Texts Appl. Math., Cambridge University, Cambridge, 2001. Search in Google Scholar

[22] A. M. Samoĭlenko and N. A. Perestyuk, Impulsive Differential Equations, World Sci. Ser. Nonlinear Sci. Ser. A Monogr. Treatises 14, World Scientific, River Edge, 1995. 10.1142/9789812798664Search in Google Scholar