Approximate Controllability of Nonlinear Stochastic Integrodifferential Third Order Dispersion System
D. N. Chalishajar, R. K. George and A. K. Nandakumaran, Exact controllability of the third order nonlinear dispersion system, Journal of Mathematical Analysis and Applications 332 (2007), 1028 – 1044.
D. N. Chalishajar, Controllability of nonlinear integro-differential third order dispersion system, Journal of Mathematical Analysis and Applications 348 (2008), 480 – 486.
A. Debussche and J. Printems, Numerical simulation of the stochastic Korteweg-de Vries equation, Physica D 134 (1999), 200 – 226.
R. Herman, The stochastic, Damped Korteweg-de Vries equation (1990), Journal of Physics A: Mathematical and General 23 (1990), 1063 – 1084.
J.M. Jeong and H.H. Roh, Approximate controllability for semilinear retarded systems, Journal of Mathematical Analysis and Applications 321 (2006), 961 – 975.
J. Klamka, Stochastic controllability of linear systems with delay in control, Bulletin of the Polish Academy of Sciences 55 (2007), 23 – 29.
G. Lin, L. Grinberg and G.E. Karniadakis, Numerical studies of the stochastic Korteweg-de Vries equation, Journal of Computational Physics 213 (2006), 676 – 703.
X. Mao, Stochastic Differential Equations and Applications, Chichester, Horwood (1997).
P. Muthukumar and P. Balasubramaniam, Approximate controllability for semi-linear retarded stochastic systems in Hilbert spaces, IMA Journal of Mathematical Control and Information 26 (2009), 131 – 140.
P. Muthukumar and C. Rajivganthi, Approximate Controllability of stochastic nonlinear third order dispersion equation, International Journal of Robust and nonlinear Control (2014), doi:10.1002/rnc.2908.
B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, Springer-Verlag, New York (1995).
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York (1983).
D.L. Russell and B.Y. Zhang, Controllability and stabilizability of the third-order linear dispersion equation on a periodic domain, SIAM Journal on Control and Optimization 31 (1993), 659 – 676.
D.L. Russell, Exact controllability and stabilizability of the Korteweg-de Vries equation, Transactions of the American Mathematical Society 348 (1996), 3643 – 3672.
R. Sakthivel, N.I. Mahmudov and Y. Ren, Approximate controllability of the nonlinear third-order dispersion equation, Applied Mathematics and Computation 217 (2011), 8507 – 8511.
L. Shen and J. Sun, Approximate controllability of abstract stochastic impulsive systems with multiple time-varying delays, International Journal of Robust and Nonlinear Control, (2012) doi:10.1002/rnc.2789.
N.K. Tomar and N. Sukavanam, Exact controllability of semilinear third order dispersion equation, The Journal of Nonlinear Sciences and Applications 4 (2011), 308 – 314.
M. Wadati, Stochastic Korteweg-de Vries equation, Journal of the Physical Society of Japan 52 (1983), 2642 – 2648.
M. Wadati and Y. Akutsu, Stochastic Korteweg-de Vries equatiowith and without damping, Journal of the Physical Society of Japan 53 (1984), 3342 – 3350.
M. Wadati, Deformation of solitons in random media, Journal of the Physical Society of Japan 59 (1990), 4201 – 4203.
H. Washimi and T. Taniuti, Propagation of ion-acoustic solitary waves of small amplitude, Physical Review Letters 17 (1996), 996 – 998.
Y.C. Xie, Exact solutions for stochastic KdV equations, Physics Letters A 310 (2003), 161 – 167.
B.Y. Zhang, Exact boundary controllability of the KdV equations, SIAM Journal on Control and Optimization 37 (1999), 523 – 565.
H.X. Zhou, Approximate controllability for a class of semilinear abstract equations, SIAM Journal on Control and Optimization 21 (1983), 551 – 565.
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