Construction of a Control for the Cubic Semilinear Heat Equation

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...

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Bibliographic Details
Published inVietnam journal of mathematics Vol. 44; no. 3; pp. 587 - 601
Main Author Vo, Thi Minh Nhat
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.09.2016
Springer Nature B.V
Springer
Subjects
Analysis of PDEs
Boundary conditions
Controllability
Mathematics
Mathematics and Statistics
Thermodynamics
Null controllability
Linear heat equation
Cubic semilinear heat equation
Secondary 93B05
Primary 35K58
cubic semilinear heat equation
null controllability
Secondary: 93B05
linear heat equa-tion 2010 Mathematics Subject Classification Primary: 35K58
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ISSN2305-221X
2305-2228
DOI10.1007/s10013-015-0171-x

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Summary: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.
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ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-015-0171-x