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References (25)
-
M. Wadati, Y. Akutsu (1984)
Stochastic Korteweg-de Vries Equation with and without DampingJournal of the Physical Society of Japan, 53
-
N. Tomar, N. Sukavanam (2011)
EXACT CONTROLLABILITY OF SEMILINEAR THIRD ORDER DISPERSION EQUATIONThe Journal of Nonlinear Sciences and Applications, 04
-
R. Sakthivel, N. Mahmudov, Yong Ren (2011)
Approximate controllability of the nonlinear third-order dispersion equationAppl. Math. Comput., 217
-
D. Russell, Bingyu Zhang (1996)
Exact controllability and stabilizability of the Korteweg-de Vries equationTransactions of the American Mathematical Society, 348
-
(1983)
Semigroups of Linear Operators and Applications to Partial Differential Equations -
Lijuan Shen, Jitao Sun (2013)
Approximate controllability of abstract stochastic impulsive systems with multiple time‐varying delaysInternational Journal of Robust and Nonlinear Control, 23
-
R. Herman (1990)
The stochastic, damped KdV equationJournal of Physics A, 23
-
Wadati (1983)
Stochastic Korteweg-de Vries equationJournal of the Physical Society of Japan, 52
-
B Oksendal (1995)
Stochastic Differential Equations: An Introduction with ApplicationsJournal of Mathematical Analysis and Applications
-
J. Jeong, Hyun-Hee Roh (2006)
Approximate controllability for semilinear retarded systemsJournal of Mathematical Analysis and Applications, 321
-
A. Debussche, J. Printems (1999)
Numerical simulation of the stochastic Korteweg-de Vries equationPhysica D: Nonlinear Phenomena, 134
-
L Shen, J Sun (2012)
Approximate controllability of abstract stochastic impulsive systems with multiple time‐varying delaysSIAM Journal on Control and Optimization
-
Yingchao Xie (2003)
Exact solutions for stochastic KdV equationsPhysics Letters A, 310
-
J. Fuerst (2016)
Stochastic Differential Equations And Applications -
D. Chalishajar (2008)
Controllability of nonlinear integro-differential third order dispersion systemJournal of Mathematical Analysis and Applications, 348
-
J. Klamka, A. Czornik (2016)
Stochastic controllability of linear systems with delay in control2016 17th International Carpathian Control Conference (ICCC)
-
G. Lin, Leopold Grinberg, G. Karniadakis (2006)
Numerical studies of the stochastic Korteweg-de Vries equationJ. Comput. Phys., 213
-
M. Wadati (1990)
Deformation of solitons in random mediaJournal of the Physical Society of Japan, 59
-
B. Øksendal (1987)
Stochastic differential equations : an introduction with applicationsJournal of the American Statistical Association, 82
-
D. Russell, Bingyu Zhang (1993)
Controllability and stabilizability of the third-order linear dispersion equation on a periodic domainSiam Journal on Control and Optimization, 31
-
H. Washimi, T. Taniuti (1966)
ON THE PROPAGATION OF ION ACOUSTIC SOLITARY WAVES OF SMALL AMPLITUDE.The annual research report, 51
-
M. Palanisamy, P. Balasubramaniam (2009)
Approximate controllability for semi-linear retarded stochastic systems in Hilbert spacesIMA J. Math. Control. Inf., 26
-
Bingyu Zhang (1999)
Exact Boundary Controllability of the Korteweg--de Vries EquationSiam Journal on Control and Optimization, 37
-
R. George, D. Chalishajar, A. Nandakumaran (2007)
Exact controllability of the nonlinear third-order dispersion equationJournal of Mathematical Analysis and Applications, 332
-
Hongying Zhou (1983)
Approximate Controllability for a Class of Semilinear Abstract EquationsSiam Journal on Control and Optimization, 21
- Publisher
- Wiley
- Copyright
- Copyright © 2014 John Wiley & Sons, Ltd.
- ISSN
- 1049-8923
- eISSN
- 1099-1239
- DOI
- 10.1002/rnc.2908
- Publisher site
- See Article on Publisher Site
Abstract
In this work, we consider a class of control systems governed by the stochastic nonlinear third‐order dispersion equation in Hilbert spaces. We first prove the existence of mild solutions of stochastic nonlinear third‐order dispersion equation by using fixed point theory, infinite dimensional semigroup properties, stochastic analysis techniques, and then a new set of sufficient conditions are formulated which guarantees the approximate controllability of the main problem. Finally, an example is provided to illustrate the application of the obtained results.Copyright © 2012 John Wiley & Sons, Ltd.
Journal
International Journal of Robust and Nonlinear Control – Wiley
Published: Jan 1, 2014
Keywords: ; ; ; ;