Quasilinear hyperbolic equations with hysteresis

Augusto Visintin

Displaying similar documents to “Quasilinear hyperbolic equations with hysteresis”

Quasilinear hyperbolic equations with hysteresis

Augusto Visintin (2002)

Annales de l'I.H.P. Analyse non linéaire

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Resonance in Preisach systems

Pavel Krejčí (2000)

Applications of Mathematics

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This paper deals with the asymptotic behavior as $t \to \infty$ of solutions $u$ to the forced Preisach oscillator equation $\ddot{w} (t) + u (t) = ψ (t)$ , $w = u + 𝒫 [u]$ , where $𝒫$ is a Preisach hysteresis operator, $ψ \in L^{\infty} (0, \infty)$ is a given function and $t \geq 0$ is the time variable. We establish an explicit asymptotic relation between the Preisach measure and the function $ψ$ (or, in a more physical terminology, a balance condition between the hysteresis dissipation and the external forcing) which guarantees that every solution remains bounded for all times. Examples...

Well-posedness and regularity for a parabolic-hyperbolic Penrose-Fife phase field system

Elisabetta Rocca (2005)

Applications of Mathematics

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This work is concerned with the study of an initial boundary value problem for a non-conserved phase field system arising from the Penrose-Fife approach to the kinetics of phase transitions. The system couples a nonlinear parabolic equation for the absolute temperature with a nonlinear hyperbolic equation for the phase variable $χ$ , which is characterized by the presence of an inertial term multiplied by a small positive coefficient $μ$ . This feature is the main consequence of supposing...