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A Variational Approach to Neumann Stochastic Semi-Linear Equations Modeling the Thermostatic Control

Author

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  • Ioana Ciotir

    (Iasi Branch of the Romanian Academy
    Laboratoire de Mathématiques de l’INSA de Rouen)

Abstract

In the present paper, we prove existence and uniqueness of a mild solution for a stochastic semi-linear equation with Neumann boundary conditions, using only general monotonicity assumptions. The study of this equation is motivated by physical applications as the model of the temperature control through the boundary. The result is proved by using an optimal control approach based on the variational principle of Brezis and Ekeland.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:3:d:10.1007_s10957-015-0787-8
    DOI: 10.1007/s10957-015-0787-8
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    References listed on IDEAS

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    1. Viorel Barbu & Stefano Bonaccorsi & Luciano Tubaro, 2015. "A Stochastic Heat Equation with Nonlinear Dissipation on the Boundary," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 317-343, May.
    2. 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.
    3. Gabriela Marinoschi, 2012. "Existence of Solutions to Time-Dependent Nonlinear Diffusion Equations via Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 792-817, September.
    Full references (including those not matched with items on IDEAS)

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