Exact controllability of the wave equation with Neumann boundary condition and time-dependent coefficients
Marcelo Moreira Cavalcanti (1999)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Marcelo Moreira Cavalcanti (1999)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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J. J. Díaz, A. M. Ramos (1995)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Jesús Ildefonso Díaz, Víctor García (2007)
RACSAM
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E. Zerrik, R. Larhrissi, H. Bourray (2007)
International Journal of Applied Mathematics and Computer Science
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The paper aims at extending the notion of regional controllability developed for linear systems cite to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder's fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated...
George Avalos, Irena Lasiecka (2003)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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The null controllability problem for a structurally damped abstract wave equation –often referred to in the literature as a structurally damped equation– is considered with a view towards obtaining optimal rates of blowup for the associated minimal energy function , as terminal time . Key use is made of the underlying analyticity of the semigroup generated by the elastic operator , as well as of the explicit characterization of its domain of definition. We ultimately find that the...
Alexander Y. Khapalov (2002)
ESAIM: Control, Optimisation and Calculus of Variations
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We study the global approximate controllability of the one dimensional semilinear convection-diffusion-reaction equation governed in a bounded domain via the coefficient (bilinear control) in the additive reaction term. Clearly, even in the linear case, due to the maximum principle, such system is not globally or locally controllable in any reasonable linear space. It is also well known that for the superlinear terms admitting a power growth at infinity the global approximate controllability...
Benabdallah, Assia, Naso, Maria Grazia (2002)
Abstract and Applied Analysis
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A. Y. Khapalov (1999)
Revista Matemática Complutense
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We discuss several global approximate controllability properties for the semilinear heat equation with superlinear reaction-convection term, governed in a bounded domain by locally distributed controls. First, based on the asymptotic analysis in vanishing time, we study the steering of the projections of its solution on any finite dimensional space spanned by the eigenfunctions for the truncated linear part. We show that, if the control-supporting area is properly chosen, then they...