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Stability for dissipative magneto-elastic systems

Reinhard Racke (2003)

Banach Center Publications

In this survey we first recall results on the asymptotic behavior of solutions in classical thermoelasticity. Then we report on recent results in linear magneto-thermo-elasticity and magneto-elasticity, respectively.

Stabilization of a layered piezoelectric 3-D body by boundary dissipation

Boris Kapitonov, Bernadette Miara, Gustavo Perla Menzala (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a linear coupled system of quasi-electrostatic equations which govern the evolution of a 3-D layered piezoelectric body. Assuming that a dissipative effect is effective at the boundary, we study the uniform stabilization problem. We prove that this is indeed the case, provided some geometric conditions on the region and the interfaces hold. We also assume a monotonicity condition on the coefficients. As an application, we deduce exact controllability of the system with boundary control...

The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory

Ammar Derbazi, Mohamed Dalah, Amar Megrous (2016)

Applications of Mathematics

We study a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The material is assumed to be electro-viscoelastic with long-term memory, and the friction is modeled with Tresca's law and the foundation is assumed to be electrically conductive. First we derive the classical variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field with a time-dependent...

Una teoria di piastra laminata piezoelettrica

Paolo Bisegna (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

È presentato un modello di piastra laminata piezoelettrica, dedotto razionalmente dalla teoria tridimensionale della piezoelettricità di Voigt. Si tratta di un'estensione ai laminati piezoelettrici della teoria di laminato elastico detta «alla Reissner-Mindlin». Le equazioni che governano il problema del laminato piezoelettrico sono fornite sia in forma differenziale che in forma variazionale. Il modello proposto è utilizzato nell'analisi di alcuni semplici problemi, allo scopo di saggiarne l'affidabilità....

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