73
Views
7
CrossRef citations to date
0
Altmetric
Research Articles

Interior approximate controllability of second-order semilinear control systems

&
Pages 615-624 | Received 16 Dec 2021, Accepted 12 Dec 2022, Published online: 02 Jan 2023

References

  • Arora, U., & Sukavanam, N. (2015). Approximate controllability of second order semilinear stochastic system with nonlocal conditions. Applied Mathematics and Computation, 258, 111–119. https://doi.org/10.1016/j.amc.2015.01.118
  • Balachandran, K., & Anthoni, S. M. (2001). Controllability of second-order semilinear neutral functional differential systems in Banach spaces. Computers & Mathematics with Applications, 41(10–11), 1223–1235. https://doi.org/10.1016/S0898-1221(01)00093-1
  • Balachandran, K., Park, J. Y., & Anthoni, S. M. (1999). Controllability of second order semilinear Volterra integrodifferential systems in Banach spaces. Bulletin of the Korean Mathematical Society, 36(1), 1–13.
  • Balasubramaniam, P., & Muthukumar, P. (2009). Approximate controllability of second-order stochastic distributed implicit functional differential systems with infinite delay. Journal of Optimization Theory and Applications, 143(2), 225–244. https://doi.org/10.1007/s10957-009-9564-x
  • Dineshkumar, C., Udhayakumar, R., Vijayakumar, V., & Nisar, K. S. (2021). A discussion on the approximate controllability of Hilfer fractional neutral stochastic integro-differential systems. Chaos, Solitons & Fractals, 142, 110472. https://doi.org/10.1016/j.chaos.2020.110472
  • Ding, Y., & Li, Y. (2020). Finite-approximate controllability of fractional stochastic evolution equations with nonlocal conditions. Journal of Inequalities and Applications, 2020(1), 1–24. https://doi.org/10.1186/s13660-019-2265-6
  • Fabre, C., Puel, J.-P., & Zuazua, E. (1995). Approximate controllability of the semilinear heat equation. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 125(1), 31–61. https://doi.org/10.1017/S0308210500030742
  • Henríquez, H. R., & Hernández, E. (2009). Approximate controllability of second-order distributed implicit functional systems. Nonlinear Analysis: Theory, Methods and Applications, 70(2), 1023–1039. https://doi.org/10.1016/j.na.2008.01.029
  • Hernández, E., Azevedo, K. A., & O'Regan, D. (2018). On second order differential equations with state-dependent delay. Applicable Analysis, 97(15), 2610–2617. https://doi.org/10.1080/00036811.2017.1382685
  • Hernández, E., Henríquez, H. R., & McKibben, M. A. (2009). Existence results for abstract impulsive second-order neutral functional differential equations. Nonlinear Analysis: Theory, Methods and Applications, 70(7), 2736–2751. https://doi.org/10.1016/j.na.2008.03.062
  • Joshi, M. C., & Bose, R. K. (1985). Some topics in nonlinear functional analysis. A Halsted Press Book. John Wiley & Sons, Inc. viii+311 pp. ISBN: 0-470-20024-3.
  • Kavitha, K., Nisar, K. S., Shukla, A., Vijayakumar, V., & Rezapour, S. (2021). A discussion concerning the existence results for the Sobolev-type Hilfer fractional delay integro-differential systems. Advances in Difference Equations, 2021(1), 1–18. https://doi.org/10.1186/s13662-021-03624-1
  • Kumar, A., Vats, R. K., & Kumar, A. (2020). Approximate controllability of second-order non-autonomous system with finite delay. Journal of Dynamical and Control Systems, 26(4), 611–627. https://doi.org/10.1007/s10883-019-09475-0
  • Kumar, S., & Sukavanam, N. (2014). Controllability of second-order systems with nonlocal conditions in Banach spaces. Numerical Functional Analysis and Optimization, 35(4), 423–431. https://doi.org/10.1080/01630563.2013.814067
  • Leiva, H. (2008). Interior controllability of a broad class of second order equations in L2(Ω). Revista Notas de Mathematoca, 4(1), 49–59.
  • Leiva, H., Merentes, N., & Sanchez, J. L. (2011). Interior controllability of the nD semilinear heat equation. African Diaspora Journal of Mathematics, 12(2), 1–12.
  • Leiva, H., & Quintana, Y. (2009). Interior controllability of a broad class of reaction diffusion equations. Mathematical Problems in Engineering, Art ID 708516. https://doi.org/10.1155/2009/708516
  • Ma, Y.-K., Mohan Raja, M., Nisar, K. S., Shukla, A., & Vijayakumar, V. (2022). Results on controllability for Sobolev type fractional differential equations of order 1<r<2 with finite delay. AIMS Mathematics, 7(6), 10215–10233. https://doi.org/10.3934/math.2022568
  • McKibben, M. A. (2003). Approximate controllability for a class of abstract second-order functional evolution equations. Journal of Optimization Theory and Applications, 117(2), 397–414. https://doi.org/10.1023/A:1023639908792
  • Mohan Raja, M., & Vijayakumar, V. (2022). Optimal control results for Sobolev-type fractional mixed Volterra–Fredholm type integrodifferential equations of order 1<r<2 with sectorial operators. Optimal Control Applications and Methods, 43(5), 1314–1327. https://doi.org/10.1002/oca.v43.5
  • Mohan Raja, M., Vijayakumar, V., Shukla, A., Nisar, K. S., & Rezapour, S. (2021). New discussion on nonlocal controllability for fractional evolution system of order 1<r<2. Advances in Difference Equations, 2021(1), 1–19. https://doi.org/10.1186/s13662-021-03630-3
  • Mohan Raja, M., Vijayakumar, V., Shukla, A., Sooppy Nisar, K., Sakthivel, N., & Kaliraj, K. (2022). Optimal control and approximate controllability for fractional integrodifferential evolution equations with infinite delay of order r∈(1,2). Optimal Control Applications and Methods, 43(4), 996–1019. https://doi.org/10.1002/oca.v43.4
  • Naito, K. (1987). Controllability of semilinear control systems dominated by the linear part. SIAM Journal on Control and Optimization, 25(3), 715–722. https://doi.org/10.1137/0325040
  • Nisar, K. S., & Vijayakumar, V. (2022). An analysis concerning approximate controllability results for second-order Sobolev-type delay differential systems with impulses. Journal of Inequalities and Applications, 2022(1), 1–26. https://doi.org/10.1186/s13660-022-02791-3
  • Patel, R., Shukla, A., Nieto, J. J., Vijayakumar, V., & Jadon, S. S. (2022). New discussion concerning to optimal control for semilinear population dynamics system in Hilbert spaces. Nonlinear Analysis: Modelling and Control, 27(3), 496–512. https://doi.org/10.15388/namc.2022.27.26407
  • Patel, R., Vijayakumar, V., Nieto, J. J., Jadon, S. S., & Shukla, A. (2022). A note on the existence and optimal control for mixed Volterra–Fredholm-type integrodifferential dispersion system of third order. Asian Journal of Control, 1–9. https://doi.org/10.1002/asjc.2860.
  • Pazy, A. (1983). Semigroups of linear operators and applications to partial differential equations. Applied mathematical sciences: Vol. 44. Springer-Verlag. viii+279 pp. ISBN: 0-387-90845-5.
  • Sakthivel, R., Anandhi, E. R., & Mahmudov, N. I. (2008). Approximate controllability of second-order systems with state-dependent delay. Numerical Functional Analysis and Optimization, 29(11–12), 1347–1362. https://doi.org/10.1080/01630560802580901
  • Shukla, A., Sukavanam, N., & Pandey, D. N. (2015). Approximate controllability of semilinear stochastic control system with nonlocal conditions. Nonlinear Dynamics and Systems Theory, 15(3), 321–333.
  • Shukla, A., Sukavanam, N., & Pandey, D. N. (2016). Complete controllability of semilinear stochastic systems with delay in both state and control. Mathematical Reports (Bucuresti), 18(2), 247–259.
  • Shukla, A., Sukavanam, N., & Pandey, D. N. (2018). Controllability of semilinear stochastic control system with finite delay. IMA Journal of Mathematical Control and Information, 35(2), 427–449. https://doi.org/10.1093/imamci/dnw059
  • Shukla, A., Vijayakumar, V., & Nisar, K. S. (2022). A new exploration on the existence and approximate controllability for fractional semilinear impulsive control systems of order r∈(1,2). Chaos, Solitons & Fractals, 154, 111615. https://doi.org/10.1016/j.chaos.2021.111615
  • Vijayakumar, V. (2018a). Approximate controllability results for impulsive neutral differential inclusions of Sobolev-type with infinite delay. International Journal of Control, 91(10), 2366–2386. https://doi.org/10.1080/00207179.2017.1346300
  • Vijayakumar, V. (2018b). Approximate controllability results for abstract neutral integro-differential inclusions with infinite delay in Hilbert spaces. IMA Journal of Mathematical Control and Information, 35(1), 297–314. https://doi.org/10.1093/imamci/dnw049
  • Vijayakumar, V., Ravichandran, C., & Murugesu, R. (2013). Nonlocal controllability of mixed Volterra–Fredholm type fractional semilinear integro-differential inclusions in Banach spaces. Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 20(4–5), 485–502.
  • Vijayakumar, V., Udhayakumar, R., & Dineshkumar, C. (2021). Approximate controllability of second order nonlocal neutral differential evolution inclusions. IMA Journal of Mathematical Control and Information, 38(1), 192–210. https://doi.org/10.1093/imamci/dnaa001
  • You, Z., Feckan, M., & Wang, J. R. (2020). Relative controllability of fractional delay differential equations via delayed perturbation of Mittag–Leffler functions. Journal of Computational and Applied Mathematics, 378, 112939. https://doi.org/10.1016/j.cam.2020.112939
  • Zhang, M., & Gao, H. (2018). Interior controllability of semi-linear degenerate wave equations. Journal of Mathematical Analysis and Applications, 457(1), 10–22. https://doi.org/10.1016/j.jmaa.2017.07.057

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.