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Vietnam Journal of Mathematics

, Volume 44, Issue 3, pp 587–601 | Cite as

Construction of a Control for the Cubic Semilinear Heat Equation

  • Thi Minh Nhat VoEmail author
Article
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Abstract

In this article, we consider the null controllability problem for the cubic semilinear heat equation in bounded domains Ω of ℝ n , n ≥ 3 with Dirichlet boundary conditions for small initial data. A constructive way to compute a control function acting on any nonempty open subset ω of Ω is given such that the corresponding solution of the cubic semilinear heat equation can be driven to zero at a given final time T. Furthermore, we provide a quantitative estimate for the smallness of the size of the initial data with respect to T that ensures the null controllability property.

Keywords

Null controllability Cubic semilinear heat equation Linear heat equation 

Mathematics Subject Classification (2010)

Primary 35K58 Secondary 93B05 

Notes

Acknowledgments

The author would like to express her gratitude to both referees of this journal for the valuable comments, important suggestions, and corrections of this work which improved substantially the first version of this article.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  1. 1.Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS UMR 7539, Institut GaliléeVilletaneuse CedexFrance
  2. 2.Université d’Orléans, Laboratoire MAPMO, CNRS UMR 7349, Fédération Denis Poisson, FR CNRS 2964, Bâtiment de MathématiquesOrléans Cedex 2France
  3. 3.Ho Chi Minh City University of Natural ScienceHo Chi Minh CityVietnam

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