Kirchhoff-Carrier elastic strings in noncylindrical domains.
Limaco Ferrel, J., Medeiros, L.A. (1999)
Portugaliae Mathematica
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Limaco Ferrel, J., Medeiros, L.A. (1999)
Portugaliae Mathematica
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Rabah Bey, Amar Heminna, Jean-Pierre Lohéac (2003)
Revista Matemática Complutense
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We propose a direct approach to obtain the boundary stabilization of the isotropic linear elastodynamic system by a natural feedback; this method uses local coordinates in the expression of boundary integrals as a main tool. It leads to an explicit decay rate of the energy function and requires weak geometrical conditions: for example, the spacial domain can be the difference of two star-shaped sets.
Clark, M.R., Lima, O.A. (1997)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Kais Ammari, Marius Tucsnak (2001)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.
Rabello, Tania Nunes, de Campos Vieira, Maria Cristina (2005)
Journal of Inequalities and Applications [electronic only]
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Jemal Peradze (2004)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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The initial boundary value problem for a beam is considered in the Timoshenko model. Assuming the analyticity of the initial conditions, it is proved that the problem is solvable throughout the time interval. After that, a numerical algorithm, consisting of three steps, is constructed. The solution is approximated with respect to the spatial and time variables using the Galerkin method and a Crank–Nicholson type scheme. The system of equations obtained by discretization is solved by...
Piermarco Cannarsa, Vilmos Komornik, Paola Loreti (1999)
ESAIM: Control, Optimisation and Calculus of Variations
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Mikulevicius, R., Valiukevicius, G. (2000)
Electronic Journal of Probability [electronic only]
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Krylov, N.V. (2000)
Electronic Journal of Probability [electronic only]
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Hélène Rouzaud (2003)
Revista Matemática Complutense
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This article is devoted to the study of a flame ball model, derived by G. Joulin, which satisfies a singular integro-differential equation. We prove that, when radiative heat losses are too important, the flame always quenches; when heat losses are smaller, it stabilizes or quenches, depending on an energy input parameter. We also examine the asymptotics of the radius for these different regimes.
Mesloub, Said, Lekrine, Nadia (2001)
Matematichki Vesnik
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