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Carleman estimates for degenerate parabolic operators with applications to null controllability
Abstract.We prove an estimate of Carleman type for the one dimensional heat equation $$ u_t - \left( {a\left( x \right)u_x } \right)_x + c\left( {t,x} \right)u = h\left( {t,x} \right),\quad \left(Expand
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Convexity and Weighted Integral Inequalities for Energy Decay Rates of Nonlinear Dissipative Hyperbolic Systems
Abstract This work is concerned with the stabilization of hyperbolic systems by a nonlinear feedback which can be localized on a part of the boundary or locally distributed. We show that generalExpand
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A general method for proving sharp energy decay rates for memory-dissipative evolution equations
Abstract This Note is concerned with stabilization of hyperbolic systems by a distributed memory feedback. We present here a general method which gives energy decay rates in terms of the asymptoticExpand
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Decay estimates for second order evolution equations with memory
Abstract This paper develops a unified method to derive decay estimates for general second order integro-differential evolution equations with semilinear source terms. Depending on the properties ofExpand
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Internal Controllability of First Order Quasi-linear Hyperbolic Systems with a Reduced Number of Controls
In this paper we investigate the exact controllability of $n \times n$ first order one-dimensional quasi-linear hyperbolic systems by internal controls that are localized in space in some part of the domain. Expand
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Asymptotic behavior for Timoshenko beams subject to a single nonlinear feedback control
Abstract.We consider systems of Timoshenko type in a one-dimensional bounded domain. The physical system is damped by a single feedback force, only in the equation for the rotation angle, no directExpand
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Indirect Boundary Stabilization of Weakly Coupled Hyperbolic Systems
This work is concerned with the boundary stabilization of an abstract system of two coupled second order evolution equations wherein only one of the equations is stabilized (indirect damping). Expand
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A Two-Level Energy Method for Indirect Boundary Observability and Controllability of Weakly Coupled Hyperbolic Systems
This work is concerned with the boundary observability of an abstract system of two coupled second order evolution equations, the coupling operator being a compact perturbation of the uncoupled system. Expand
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We study in an abstract setting the indirect stabilization of systems of two wave-like equations coupled by a localized zero order term. Only one of the two equations is directly damped. The mainExpand
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Indirect controllability of locally coupled wave-type systems and applications
Abstract We consider symmetric systems of two wave-type equations only one of them being controlled. The two equations are coupled by zero order terms, localized in part of the domain. We prove anExpand
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