Browsing by Author "Fernandez, Claudio"

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    Commutator methods for unitary operators
    (2013) Fernandez, Claudio; Richard, Serge; de Aldecoa, Rafael Tiedra
    We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local finiteness of point spectrum. Large families of locally smooth operators are also exhibited. Half of the paper is dedicated to applications, and a special emphasis is put on the study of cocycles over irrational rotations. It is apparently the first time that commutator methods are applied in the context of rotation algebras, for the study of their generators.
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    Exponential decay and resonances in a driven system
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2012) Briet, Philippe; Fernandez, Claudio
    We study the resonance phenomena for time periodic perturbations of a Hamiltonian H on the Hilbert space L-2 (R-d). Here, resonances are characterized in terms of time behavior of the survival probability. Our approach uses the Floquet-Howland formalism combined with the results of L. Cattaneo, J.M. Graf and W. Hunziker on resonances for time independent perturbations. (C) 2012 Elsevier Inc. All rights reserved.
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    Maximal Regularity for Flexible Structural Systems in Lebesgue Spaces
    (HINDAWI LTD, 2010) Fernandez, Claudio; Lizama, Carlos; Poblete, Veronica
    We study abstract equations of the form lambda u'''(t) + u"(t) = c(2) Au(t) + c(2)mu Au'(t) + f (t), 0 < lambda < mu which is motivated by the study of vibrations of flexible structures possessing internal material damping. We introduce the notion of (alpha;beta;gamma)-regularized families, which is a particular case of (a; k)-regularized families, and characterize maximal regularity in L-p-spaces based on the technique of Fourier multipliers. Finally, an application with the Dirichlet-Laplacian in a bounded smooth domain is given.
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    Regularity of solutions for a third order differential equation in Hilbert spaces
    (ELSEVIER SCIENCE INC, 2011) Fernandez, Claudio; Lizama, Carlos; Poblete, Veronica
    We study regularity of mild and strong solutions of an abstract mathematical model of a flexible space structure under appropriate initial conditions. We apply our results showing qualitative properties of the trajectories in the case of the negative Laplacian operator. (C) 2011 Elsevier Inc. All rights reserved.
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    SPECTRAL PROPERTIES OF A COUPLED SYSTEM OF SCHRODINGER EQUATIONS WITH TIME-PERIODIC COEFFICIENTS
    (KHAYYAM PUBL CO INC, 2012) Coimbra Charao, R.; Perla Menzala, G.; Angelica Astaburuaga, M.; Fernandez, Claudio
    We consider a coupled system of Schrodinger equations with time-periodic coefficients
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    Stabilization of the wave equation with Neumann boundary condition and localized nonlinear damping
    (EUDOXUS PRESS, LLC, 2009) Charao, Ruy C.; Astaburuaga, Maria A.; Fernandez, Claudio
    We show that the solutions of the wave equation with potential, Neumann boundary conditions and a locally distributed nonlinear damping, decay to zero, with an algebraic rate, that is, the total energy E(t) satisfies for t >= 0: E(t) <= C(1 + t)(-gamma), where C is a positive constant depending on E(0) and gamma > 0 is a constant. We assume geometrical conditions as in P. Martinez [7]. In the one/two-dimensional cases, we obtain exponential decay rate when the nonlinear dissipation behaves linearly close to the origin. The same result holds in higher dimension if the dissipative localized term behaves linearly.