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Approximate controllability of stochastic nonlinear third-order dispersion equation

Authors

  • P. Muthukumar,

    Corresponding author
    1. Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram - 624 302, Tamilnadu, India
    • Correspondence to: P. Muthukumar, IUSSTF Research Fellow, Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram - 624 302, Tamilnadu, India.

      E-mail: pmuthukumargri@gmail.com

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  • C. Rajivganthi

    1. Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram - 624 302, Tamilnadu, India
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SUMMARY

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.

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