Warianty tytułu
Języki publikacji
Abstrakty
In this paper, we establish a result concerning the controllability of a mixed Volterra–Fredholm type integrodifferential third order dispersion equation. The result is obtained by using the theory of strongly continuous semigroups and the Banach fixed point theorem.
Czasopismo
Rocznik
Tom
Strony
1--7
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
- Department of Mathematics, Indian Institute of Technology, Roorkee-247667, Uttarakhand, India
autor
- Department of Mathematics, Indian Institute of Technology, Roorkee-247667, Uttarakhand, India
Bibliografia
- [1] K. Balachandran and E. R. Anandhi, Boundary controllability of integrodifferential systems in Banach spaces, Proc. Indian Acad. Sci. Math. Sci 111 (2001), no. 1, 127–135.
- [2] K. Balachandran and R. Sakthivel, Controllability of functional semilinear integrodifferential systems in Banach spaces, J. Math. Anal. Appl. 255 (2001), no. 2, 447–457.
- [3] D. N. Chalishajar, Controllability of mixed Volterra–Fredholm type integro-differential systems in Banach space, J. Franklin Inst. 344 (2007), no. 1, 12–21.
- [4] D. N. Chalishajar, Controllability of nonlinear integro-differential third order dispersion system, J. Math. Anal. Appl. 348 (2008), no. 1, 480–486.
- [5] R. K. George, D. N. Chalishajar and A. K. Nandakumaran, Exact controllability of the third order nonlinear dispersion equation, J. Math. Anal. Appl. 332 (2007), no. 2, 1028–1044.
- [6] N. Kkelil, N. N. Bensalah and A. Zerarka, Artifcial perturbation for solving the Korteweg–de Vries equation, J. Zhejiang Univ. Sci. A 7 (2006), no. 12, 2079–2082.
- [7] D. J. Korteweg and G. de. Vries, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Phil. Mag. 39 (1895), 422–443.
- [8] B. G. Pachpatte, On mixed Volterra–Fredholm type integral equations, Indian J. Pure Appl. Math. 17 (1986), 488–496.
- [9] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, New York, 1983.
- [10] M. D. Quinn and N. Carmichael, An approach to non-linear control problems using fixed-point methods, degree theory and pseudo-inverses, Numer. Funct. Anal. Optim. 7 (1984), 197–219.
- [11] L. Rosier, Exact boundary controllability for the Korteweg–de Vries equation on a bounded domain, ESAIM Control Optim. Calc. Var. 2 (1997), 33–55.
- [12] L. Rosier, Exact boundary controllability for the linear Korteweg–de Vries equation on the half line, SIAM J. Control Optim. 39 (2000), no. 2, 331–351.
- [13] D. L. Russell and B. Y. Zhang, Controllability and stabilizability of the third-order linear dispersion equation on a periodic domain, SIAM J. Control Optim. 31 (1993), no. 3, 659–676.
- [14] D. L. Russell and B. Y. Zhang, Exact controllability and stabilizability of the Korteweg–de Vries equation, Trans. Amer. Math. Soc. 348 (1996), no. 9, 3643–3672.
- [15] L. Yushu, Time jitters caused by third-order dispersion in soliton transmission system, Int. J. Infrared Millim. Waves 20 (1999), 1541–1548.
- [16] B.-Y. Zhang, Exact boundary controllability for the Korteweg–de Vries equation, SIAM J. Control Optim. 37 (1999), no. 2, 543–565.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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