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Optimal Control Approach to Nonlinear Diffusion Equations Driven by Wiener Noise

Author

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  • Viorel Barbu

    (Octav Mayer Institute of Mathematics of Romanian Academy)

Abstract

The stochastic nonlinear infinite-dimensional equations of gradient type and with additive Wiener noise can be reduced to an optimal convex control problem via Brezis–Ekeland duality device. This approach is illustrated here on a few classes of nonlinear stochastic parabolic equations which are relevant as diffusion models under stochastic Gaussian perturbations, and image restoring technique.

Suggested Citation

  • Viorel Barbu, 2012. "Optimal Control Approach to Nonlinear Diffusion Equations Driven by Wiener Noise," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 1-26, April.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:1:d:10.1007_s10957-011-9946-8
    DOI: 10.1007/s10957-011-9946-8
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    Cited by:

    1. Ioana Ciotir, 2015. "A Variational Approach to Neumann Stochastic Semi-Linear Equations Modeling the Thermostatic Control," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 1095-1111, December.
    2. Gabriela Marinoschi, 2014. "Variational Solutions to Nonlinear Diffusion Equations with Singular Diffusivity," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 430-445, May.
    3. Barbu, Viorel & Brzeźniak, Zdzisław & Hausenblas, Erika & Tubaro, Luciano, 2013. "Existence and convergence results for infinite dimensional nonlinear stochastic equations with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 934-951.

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