Asymptotic Behaviour for a Phase-Field System with Hysteresis

A class of differential-delay systems with hysteresis: Asymptotic behaviour of solutions

A class of differential-delay systems with hysteresis is considered. Conditions ensuring boundedness of solutions and related asymptotic and integrability properties are expressed in terms of data associated with the linear component of the overall system and a Lipschitz constant associated with the hysteretic component. c © 2007 Elsevier Ltd. All rights reserved. MSC: 34K20; 34K35; 47J40; 93C10

Asymptotic behaviour of a class of inhomogeneous scalar field cosmologies

The asymptotic behaviour of a class of inhomogeneous scalar field cosmologies with a Liouville type of potential is studied. We define a set of new variables for which the phase space of the system of Einstein equations is bounded. This allows us to perform a complete analysis of the evolution of these cosmologies. We also discuss the extension of the cosmic no-hair theorem.

Time-asymptotic Behaviour of Weak Solutions for a Viscoelastic Two-phase Model with Nonlocal Capillarity

Abstract. The aim of this paper is to study the time-asymptotic behaviour of weak solutions of an initial-boundary value problem for a viscoelastic two-phase material with capillarity in one space dimension. Therein, the capillarity is modelled via a nonlocal interaction potential. Based on the existence and regularity results of [5], we analyze the time-asymptotic convergence of the strain-vel...

A Simple Model for Three Phase Flow with Hysteresis

Dynamical Hysteresis without Static Hysteresis: Scaling Laws and Asymptotic Expansions

We study dynamical hysteresis in a simple class of nonlinear ordinary differential equations, namely first-order equations subject to sinusoidal forcing. The assumed nonlinearities are such that the area of the hysteresis loop vanishes as the forcing frequency tends to zero; in other words, there is no static hysteresis. Using regular and singular perturbation techniques, we derive the first te...