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

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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.

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Acknowledgments

This work was supported by the Romanian National Authority for Scientific Research, CNCS-UEFISCDI (Romania) grant PN-II-RU-PD-2012-3-0240. The author would like to thank Professor Viorel Barbu for helpful comments and the anonymous referee for constructive suggestions.

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  1. Ioana Ciotir

    Present address: Laboratoire de Mathématiques de l’INSA de Rouen, Av. de l’Université, BP 08, 76801, St Etienne du Rouvray Cedex, France

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  1. Institute of Mathematics “Octav Mayer”, Iasi Branch of the Romanian Academy, Iasi, Romania

    Ioana Ciotir

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  1. Ioana Ciotir
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Ciotir, I. A Variational Approach to Neumann Stochastic Semi-Linear Equations Modeling the Thermostatic Control. J Optim Theory Appl 167, 1095–1111 (2015). https://doi.org/10.1007/s10957-015-0787-8

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  • DOI: https://doi.org/10.1007/s10957-015-0787-8

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