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- W2019664900 abstract "Abstract This Note deals with the computation of distributed null controls for a semi-linear 1D heat equation, in the sublinear and slightly superlinear cases. Under sharp growth assumptions, the existence of controls has been obtained in [E. Fernandez-Cara, E. Zuazua, Null and approximate controllability for weakly blowing up semi-linear heat equation, Ann. Inst. Henri Poincare Analyse non lineaire 17 (5) (2000) 583] via a fixed point reformulation; see also [V. Barbu, Exact controllability of the superlinear heat equation, Appl. Math. Optim. Optimization, Theory and Applications 42 (1) (2000) 73]. More precisely, Carleman estimates and Kakutaniʼs theorem together ensure the existence of fixed points for a corresponding linearized control mapping. In practice, the difficulty is to extract from the Picard iterates a convergent (sub)sequence. 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." @default.
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- W2019664900 date "2011-08-01" @default.
- W2019664900 modified "2023-09-30" @default.
- W2019664900 title "Numerical null controllability of a semi-linear heat equation via a least squares method" @default.
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- W2019664900 doi "https://doi.org/10.1016/j.crma.2011.07.014" @default.
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