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Existence and approximate controllability of stochastic semilinear reaction diffusion systems

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Abstract

In this paper, the approximate controllability of an abstract model of stochastic semilinear reaction diffusion equation in Hilbert spaces is considered. The existence and uniqueness of mild solutions of stochastic semilinear reaction diffusion equation is established by using contraction mapping principle and then a new set of sufficient conditions are formulated which guarantees the approximate controllability of main problem. Finally, the results are applied to stochastic Ornstein–Uhlenbeck equation.

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Authors and Affiliations

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

    C. Rajivganthi & P. Muthukumar

  2. Department of Mathematical Sciences, College of Science, UAE University, 15551, Al-Ain, UAE

    C. Rajivganthi & F. A. Rihan

Authors
  1. C. Rajivganthi
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  2. P. Muthukumar
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  3. F. A. Rihan
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Corresponding author

Correspondence to C. Rajivganthi.

Additional information

This work was supported by National Board for Higher Mathematics, Mumbai, India under the Grant No: 2/48(5)/2013/NBHM (R.P.)/RD-II/688 dt 16.01.2014.

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Rajivganthi, C., Muthukumar, P. & Rihan, F.A. Existence and approximate controllability of stochastic semilinear reaction diffusion systems. Int. J. Dynam. Control 5, 653–660 (2017). https://doi.org/10.1007/s40435-015-0208-8

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  • DOI: https://doi.org/10.1007/s40435-015-0208-8

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