Approximate controllability and its well-posedness for the semilinear reaction-diffusion equation with internal lumped controls
Alexander Khapalov (1999)
ESAIM: Control, Optimisation and Calculus of Variations
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Alexander Khapalov (1999)
ESAIM: Control, Optimisation and Calculus of Variations
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Farid Ammar Khodja, Assia Benabdallah, Cédric Dupaix, Ilya Kostin (2005)
ESAIM: Control, Optimisation and Calculus of Variations
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We study the null controllability by one control force of some linear systems of parabolic type. We give sufficient conditions for the null controllability property to be true and, in an abstract setting, we prove that it is not always possible to control.
Kumarasamy Sakthivel, Krishnan Balachandran, Jong-Yeoul Park, Ganeshan Devipriya (2010)
Kybernetika
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In this paper, we prove the exact null controllability of certain diffusion system by rewriting it as an equivalent nonlinear parabolic integrodifferential equation with variable coefficients in a bounded interval of with a distributed control acting on a subinterval. We first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a suitable observability estimate for adjoint system with appropriate assumptions on the coefficients....
Luis Alberto Fernández, Alexander Yuri Khapalov (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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We discuss several new results on nonnegative approximate controllability for the one-dimensional Heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every moment of time. Our methods allow us to link these two types of controls to some extend. The main results include approximate controllability properties both for the static and mobile control supports.
S. Guerrero, O. Yu. Imanuvilov (2007)
Annales de l'I.H.P. Analyse non linéaire
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E. Fernández-Cara (1997)
ESAIM: Control, Optimisation and Calculus of Variations
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Benabdallah, Assia, Naso, Maria Grazia (2002)
Abstract and Applied Analysis
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Antonio López, Enrique Zuazua (1997-1998)
Séminaire Équations aux dérivées partielles
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We address three null controllability problems related to the heat equation. First we show that the heat equation with a rapidly oscillating density is uniformly null controllable as the period of the density tends to zero. We also prove that the same result holds for the finite-difference semi-discretization in space of the constant coefficient heat equation as the step size tends to zero. Finally, we prove that the null controllability of the constant coefficient heat equation...