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• W2334835265 abstract "This paper deals with the numerical computation of distributed null controls for semi-linear 1D heat equations, in the sublinear and slightly superlinear cases. Under sharp growth assumptions, the existence of controls has been obtained in [Fernandez-Cara $&$ Zuazua, Null and approximate controllability for weakly blowing up semi-linear heat equation, 2000] via a fixed point reformulation; see also [Barbu, Exact controllability of the superlinear heat equation, 2000]. More precisely, Carleman estimates and Kakutani's Theorem together ensure the existence of solutions to fixed points for an equivalent fixed point reformulated problem. A nontrivial difficulty appears when we want to extract from the associated Picard iterates a convergent (sub)sequence. In this paper, we introduce and analyze a least squares reformulation of the problem; we show that this strategy leads to an effective and constructive way to compute fixed points. We also formulate and apply a Newton-Raphson algorithm in this context. Several numerical experiments that make it possible to test and compare these methods are performed." @default.
• W2334835265 created "2016-06-24" @default.
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• W2334835265 date "2012-01-01" @default.
• W2334835265 modified "2023-10-01" @default.
• W2334835265 title "Numerical null controllability of semi-linear 1-D heat equations: Fixed point, least squares and Newton methods" @default.
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• W2334835265 doi "https://doi.org/10.3934/mcrf.2012.2.217" @default.
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