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Construction of a control for the cubic semilinear heat equation

Abstract : In this article, we consider the null controllability problem for the cubic semi-linear 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.
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https://hal.archives-ouvertes.fr/hal-01225203
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Submitted on : Monday, November 9, 2015 - 5:22:50 PM
Last modification on : Tuesday, October 12, 2021 - 5:20:13 PM
Long-term archiving on: : Wednesday, February 10, 2016 - 10:07:59 AM

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Thi Minh Nhat Vo. Construction of a control for the cubic semilinear heat equation. Vietnam Journal of Mathematics, Springer, 2015, ⟨10.1007/s10013-015-0171-x⟩. ⟨hal-01225203⟩

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