APPROXIMATE CONTROLLABILITY RESULTS FOR INTEGRO-QUASILINEAR EVOLUTION EQUATIONS VIA TRAJECTORY REACHABLE SETS

doi:10.1007/s10473-020-0208-4

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (2): 412-424.doi: 10.1007/s10473-020-0208-4

APPROXIMATE CONTROLLABILITY RESULTS FOR INTEGRO-QUASILINEAR EVOLUTION EQUATIONS VIA TRAJECTORY REACHABLE SETS

A. Vinodkumar¹, C. Loganathan², S. Vijay²

1. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore-641 112, India;
2. Department of Mathematics, Maharaja Arts and Science College, Coimbatore-641 407, Tamil Nadu, India

收稿日期:2018-05-29 修回日期:2019-09-26 出版日期:2020-04-25 发布日期:2020-05-26
通讯作者: A. Vinodkumar E-mail:vinod026@gmail.com,a_vinodkumar@cb.amrita.edu
作者简介:C.Loganathan,E-mail:clogu@rediffmail.com;S.Vijay,E-mail:vijay_ms_oty@yahoo.co.in
基金资助:
This work was supported by Science & Engineering Research Board (DST-SERB) (ECR/2015/000301) in India.

APPROXIMATE CONTROLLABILITY RESULTS FOR INTEGRO-QUASILINEAR EVOLUTION EQUATIONS VIA TRAJECTORY REACHABLE SETS

A. Vinodkumar¹, C. Loganathan², S. Vijay²

1. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore-641 112, India;
2. Department of Mathematics, Maharaja Arts and Science College, Coimbatore-641 407, Tamil Nadu, India

Received:2018-05-29 Revised:2019-09-26 Online:2020-04-25 Published:2020-05-26
Contact: A. Vinodkumar E-mail:vinod026@gmail.com,a_vinodkumar@cb.amrita.edu
Supported by:
This work was supported by Science & Engineering Research Board (DST-SERB) (ECR/2015/000301) in India.

摘要/Abstract

摘要： In this article, we study the approximate controllability results for an integro-quasilinear evolution equation with random impulsive moments under sufficient conditions. The results are obtained by the theory of C₀ semigroup of bounded linear operators on evolution equations and using trajectory reachable sets. Finally, we generalize the results too with and without fixed type impulsive moments.

关键词: Integro-quasilinear control system, random impulses, approximate controllability

Abstract: In this article, we study the approximate controllability results for an integro-quasilinear evolution equation with random impulsive moments under sufficient conditions. The results are obtained by the theory of C₀ semigroup of bounded linear operators on evolution equations and using trajectory reachable sets. Finally, we generalize the results too with and without fixed type impulsive moments.

Key words: Integro-quasilinear control system, random impulses, approximate controllability

中图分类号:

93B05

A. Vinodkumar, C. Loganathan, S. Vijay. APPROXIMATE CONTROLLABILITY RESULTS FOR INTEGRO-QUASILINEAR EVOLUTION EQUATIONS VIA TRAJECTORY REACHABLE SETS[J]. 数学物理学报(英文版), 2020, 40(2): 412-424.

A. Vinodkumar, C. Loganathan, S. Vijay. APPROXIMATE CONTROLLABILITY RESULTS FOR INTEGRO-QUASILINEAR EVOLUTION EQUATIONS VIA TRAJECTORY REACHABLE SETS[J]. Acta mathematica scientia,Series B, 2020, 40(2): 412-424.

参考文献

[1] Abbas S, Bahuguna D. Existence of solutions to quasilinear functional differential equations. Electron J Differ Equ, 2009, 164:1-8
[2] Agarwal R, Hristova S, Donal O'Regan. Exponential stability for differntial equations with random impulses at random times. Advances in Difference Equations, 2013, 2013:372
[3] Anguraj A, Wu S, Vinodkumar A. Existence and Exponential Stability of Semilinear Functional Differential Equations with Random Impulses under Non-uniqueness. Nonlinear Anal TMA, 2011, 74:331-342
[4] Anguraj A, Vinodkumar A. Existence, Uniqueness and Stability Results of Random Impulsive Semilinear Differential Systems. Nonlinear Anal Hybrid Syst, 2010, 4(3):475-483
[5] Balachandran K, Park J Y, Park S H. Controllability of nonlocal impulsive quasilinear integrodifferential systems in Banach spaces. Reports on Math Phys, 2010, 65(2):247-257
[6] Bouzahir Hassane, Fu Xianlong. Controllability of neutral functional differential equations with infinite delay. Acta Mathematica Scientia, 2013, 31B(1):73-80
[7] Debbouchea A, Baleanu D. Controllability of fractional evolution nonlocal impulsive quasilinear delay integro-differential systems. Comp Math Appl, 2011, 62:1442-1450
[8] Divya A, Sukavanam N, Shukla A. On the approximate controllability of semilinear control systems. Cogent Mathematics, 2016, 3:1266773
[9] Heard M L. A quasi linear hyperbolic integrodifferential equations related to a nonlinear string. Trans American Math Soc, 1984, 285:805-823
[10] Kato S. Nonhomogeneous quasi-linear evolution equations in Banach spaces. Nonlinear Anal, 1985, 9:1061-1071
[11] Kumar S, Sukavanam N. Approximate controllability of fractional order neutral control systems with delay. I J Nonlinear Sci, 2012, 13:454-462
[12] Lakshmikantham V, Bainov D D, Simeonov P S. Theory of Impulsive Differential Equations. Singapore:World Scientific, 1989
[13] Naito K. Controllability of semilinear control systems dominated by the linear part. SIAMJ Control Optim, 1987, 25(3):715-722
[14] Naito K, Park J Y. Approximate Controllability for Trajectories of a Delay Volterra Control System. J Optim Ther Appli, 1989, 61:271-279
[15] Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. New York:Springer-Verlag, 1983
[16] Ryu J W, Park J Y, Kwun Y C. Approximate controllability of delay Volterra control system. Bull Korean Math Soc, 1993, 30(2):277-284
[17] Samoilenko A M, Perestyuk N A. Impulsive Differential Equations. Singapore:World Scientific, 1995
[18] Tomar N K, Sukavanam N. Approximate controllability of non-densely defined semilinear delayed control systems. Nonlinear Studies, 2011, 18(2):229-234
[19] Tomar N K, Kumar S. Approximate controllability of nonlocal semilinear time-varying delay control systems. Nonlinear Dynamics and System Theory, 2012, 12(3):303-310
[20] Triggiani R. A note on the lack of exact controllability for mild solutions in Banach spaces. SIAM J Control Optim, 1977, 15:407-411
[21] Vinodkumar A, Anguraj A. Existence of random impulsive abstract neutral non-autonomous differential inclusions with delays. Nonlinear Anal Hybrid Syst, 2011, 5:413-426
[22] Anguraj A, Vinodkumar A, Malar K. Existence and Stability Results for Random Impulsive Fractional Pantograph Equations. Filomat, 2016, 30(14):3839-3854
[23] Vinodkumar A, Malar K, Gowrisankar M, Mohankumar P. Existence, uniqueness and stability of random impulsive fractional differential equations. Acta Mathematica Scientia, 2016, 36B(2):428-442
[24] Vijay S, Loganathan C, Vinodkumar A. Approximate controllability of random impulsive semilinear control systems. Nonlinear Studies, 2016, 23(2):273-280
[25] Vinodkumar A, Senthilkumar T, Li X. Robust exponential stability results for uncertain infinite delay differential systems with random impulsive moments. Advances in Difference Equations, 2018, 2018(1):39
[26] Harrat A, Nieto Juan J, Debbouche Amar. Solvability and optimal controls of impulsive Hilfer fractional delay evolution inclusions with Clarke subdifferential. Journal of Computational and Applied Mathematics, 2018, 344:725-737
[27] Agarval Ravi P, Dumitru Baleanu, Nieto Juan J, Torres Deifim F M. A survey on fuzzy fractional differential and optimal control nonlocal evolution inclusions. Journal of Computational and Applied Mathematics, 2018, 339:3-29

APPROXIMATE CONTROLLABILITY RESULTS FOR INTEGRO-QUASILINEAR EVOLUTION EQUATIONS VIA TRAJECTORY REACHABLE SETS

APPROXIMATE CONTROLLABILITY RESULTS FOR INTEGRO-QUASILINEAR EVOLUTION EQUATIONS VIA TRAJECTORY REACHABLE SETS

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