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- W2019436615 abstract "We consider the semilinear heat equation in a bounded domain of Rd, with control on a subdomain and homogeneous Dirichlet boundary conditions. We prove that the system is null-controllable at any time provided a globally defined and bounded trajectory exists and the nonlinear term grows slower than |s|log3/2(1+|s|) at infinity. We also prove that, for some nonlinearities that behave at infinity like |s|logp(1+|s|) with p>2, null controllability does not hold. Results of the same kind are proved in the context of approximate controllability. On considère l'équation de la chaleur semi-linéaire dans un domaine borné de Rd, avec contrôle dans un sous-domaine et conditions de Dirichlet homogènes au bord. Sous l'hypothèse d'éxistence d'une trajectoire globalement définie et bornée, on montre que le système est contrôlable à zéro en tout temps si le terme non linéaire croı̂t plus lentement que |s|log3/2(1+|s|) à l'infini. On démontre aussi qu'il y a des termes non linéaires qui agissent à l'infini comme |s|logp(1+|s|) avec p>2 telles que le système ne soit pas contrôlable. La question reste ouverte lorsque 3/2≤p≤2. Finalement, on démontre des résultats similaires dans le contexte de la contrôlabilité approchée." @default.
- W2019436615 created "2016-06-24" @default.
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- W2019436615 date "2000-02-01" @default.
- W2019436615 modified "2023-10-06" @default.
- W2019436615 title "Controllability for blowing up semilinear parabolic equations" @default.
- W2019436615 doi "https://doi.org/10.1016/s0764-4442(00)00115-4" @default.
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