Geodesic
Exact Controllability of Semilinear Third Order Dispersion Equation
Tomar , N. K. 1 ; Sukavanam, N.2
1 Department of Mathematics, Indian Institute of Technology, Patna-800013, India
2 Department of Mathematics, Indian Institute of Technology, Roorkee-247667, India
Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 4, p. 308-314.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, a family of nonlinear functions is given for the exact controllability of semilinear third order dispersion equation. The obtained result has been illustrated by applying it on nonlinear Korteweg-de Vries (KdV) equation.
DOI : 10.22436/jnsa.004.04.08
Classification : 93C20, 92B20, 90C90
Keywords: Exact controllability, Dispersion System, KdV Equation.

Tomar , N. K.  1 ; Sukavanam, N. 2

1 Department of Mathematics, Indian Institute of Technology, Patna-800013, India
2 Department of Mathematics, Indian Institute of Technology, Roorkee-247667, India 
@article{JNSA_2011_4_4_a7,
     author = {Tomar  , N. K.  and Sukavanam, N.},
     title = {Exact {Controllability} of {Semilinear} {Third} {Order} {Dispersion} {Equation}},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {308-314},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {2011},
     doi = {10.22436/jnsa.004.04.08},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.04.08/}
}
TY  - JOUR
AU  - Tomar  , N. K. 
AU  - Sukavanam, N.
TI  - Exact Controllability of Semilinear Third Order Dispersion Equation
JO  - Journal of nonlinear sciences and its applications
PY  - 2011
SP  - 308
EP  - 314
VL  - 4
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.04.08/
DO  - 10.22436/jnsa.004.04.08
LA  - en
ID  - JNSA_2011_4_4_a7
ER  - 
%0 Journal Article
%A Tomar  , N. K. 
%A Sukavanam, N.
%T Exact Controllability of Semilinear Third Order Dispersion Equation
%J Journal of nonlinear sciences and its applications
%D 2011
%P 308-314
%V 4
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.04.08/
%R 10.22436/jnsa.004.04.08
%G en
%F JNSA_2011_4_4_a7
Tomar  , N. K. ; Sukavanam, N. Exact Controllability of Semilinear Third Order Dispersion Equation. Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 4, p. 308-314. doi : 10.22436/jnsa.004.04.08. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.04.08/

[1] Korteweg, D. J.; Vries, G. de On the change of the form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag. , Volume 39 (1895), pp. 422-443

[2] Russell, D. L.; B. Y. Zhang Exact Controllability and Stabilizability of the Korteweg-de Vries Equation, Trans. Amer. Math. Soc. , Volume 348(9) (1996), pp. 3643-3672

[3] L. Rosier Exact Boundary Controllability for the Korteweg-de Vries Equation on a Bounded Domain, ESIAM Control Optim. Calc. Var. , Volume 2 (1997), pp. 33-55

[4] Zhang, B. Y. Exact Controllability for the Korteweg-de Vries Equation, SIAM J. Control Optim. , Volume 37(2) (1999), pp. 543-565

[5] Rosier, L. Exact Boundary Controllability for the linear Korteweg-de Vries Equation on the half line, SIAM J. Control Optim. , Volume 39(2) (2000), pp. 331-351

[6] Hizanidis, K.; Malomed, B. A; Nistazakis, H. E; Frantzeskakis, D. J. Stabilizing soliton transmission by third-order dispersion in dispersion-compensated fibre links, Pure Appl. Opt. , Volume 7(4) (1998), pp. 57-62

[7] Yushu Liu Time Jitters caused by Third-Order Dispersion in Soliton Transmission System, Int. J. Infrared and Millimeter Waves , Volume 20(8) (1999), pp. 1541-1548

[8] Kkelil, N.; Bensalah, N.; Zerarka, A. Artificial Perturbation for Solving Korteweg-de Vries Equation, J. Zhejiang Univ. Sci. , Volume 7(12) (2006), pp. 2079-2082

[9] Balachandran, K.; J. P. Dauer Controllability of Nonlinear Systems in Banach Spaces: A Survey, J. Optimization Theory and Applications , Volume 115(1) (2002), pp. 7-28

[10] Tomar, N. K.; Sukavanam, N. Approximate Controllability of Non-densely defined Semilinear Delayed Control Systems, Nonlinear Studies, Volume 18(2) (2011), pp. 229-234

[11] Dauer, J. P.; N. I. Mahmudov Approximate Controllability of Semilinear Functional Equations in Hilbert Spaces, J. Math. Anal. Appl., Volume 273 (2002), pp. 310-327

[12] Jeong, J.-M.; Kim, H.-G. Controllability for semilinear functional integrodifferential equations, Bull. Korean Math. Soc., Volume 46(3) (2009), pp. 463-475

[13] Kavitha, V. ; Arjunan, M. Mallika Controllability of impulsive Quasi-linear Fractional mixed volterra-Fredholm-type integrodifferential equations in Banach Spaces, J. Nonlineare Sci. Appl., Volume 4(2) (2011), pp. 152-159

[14] Russell, D. L.; Zhang, B. Y. Controllability and Stabilizability of the Third-order Linear Dispersion Equation on a Periodic Domain, SIAM J. Control Optim. , Volume 31(3) (1993), pp. 659-676

[15] George, R. K.; Chalishajar, D. N.; Nandakumaran, A. K. Exact Controllability of the Nonlinear Third-order Dispersion Equation, J. Math. Anal. Appl. , Volume 332 (2007), pp. 1028-1044

[16] Pazy, A. Semigroup of Linear operators and Application to Partial Differential Equations, Springer-Verlag , New York Inc., 1983

[17] Zeidler, E. Applied Fuctional Analysis: Main Principles and Their Applications, Applied Mathematical Sciences Vol. 109, Springer-Verlag , New York Inc., 1995

Cité par Sources :