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

Similarity:

Resonance in Preisach systems

Pavel Krejčí (2000)

Applications of Mathematics

Similarity:

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

Similarity:

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...

Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials

Elisabetta Rocca, Riccarda Rossi (2008)

Applications of Mathematics

Similarity:

This paper is devoted to the analysis of a one-dimensional model for phase transition phenomena in thermoviscoelastic materials. The corresponding parabolic-hyperbolic PDE system features a internal energy balance equation, governing the evolution of the absolute temperature $ϑ$ , an evolution equation for the phase change parameter $χ$ , including constraints on the phase variable, and a hyperbolic stress-strain relation for the displacement variable $𝐮$ . The main novelty of the model is that...

Evolution equations with parameter in the hyperbolic case

Jan Bochenek, Teresa Winiarska (1996)

Annales Polonici Mathematici

Similarity:

The purpose of this paper is to give theorems on continuity and differentiability with respect to (h,t) of the solution of the initial value problem du/dt = A(h,t)u + f(h,t), u(0) = u₀(h) with parameter $h \in Ω \subset ℝ^{m}$ in the “hyperbolic” case.