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Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity

Olaf Klein (2004)

Applications of Mathematics

The asymptotic behaviour for t → ∞ of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress...

Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators

Małgorzata Pułka (2012)

Discussiones Mathematicae Probability and Statistics

We study different types of asymptotic behaviour in the set of (infinite dimensional) nonhomogeneous chains of stochastic operators acting on L¹(μ) spaces. In order to examine its structure we consider different norm and strong operator topologies. To describe the nature of the set of nonhomogeneous chains of Markov operators with a particular limit behaviour we use the category theorem of Baire. We show that the geometric structure of the set of those stochastic operators which have asymptotically...

Asymptotic behaviour of solutions of difference equations in Banach spaces

Anna Kisiołek (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider the first order difference equation in a Banach space Δ x n = ∑ i = 0 ∞ a n i f ( x n + i ) . We show that this equation has a solution asymptotically equal to a. As an application of our result we study the difference equation Δ x n = ∑ i = 0 ∞ a n i g ( x n + i ) + ∑ i = 0 ∞ b n i h ( x n + i ) + y n and give conditions when this equation has solutions. In this note we extend the results from [8,9]. For example, in [9] the function f is a real Lipschitz function. We suppose that f has values in a Banach space and satisfies some conditions with respect to the measure of noncompactness...

Asymptotic behaviour of stochastic quasi dissipative systems

Giuseppe Da Prato (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.

Asymptotic behaviour of stochastic quasi dissipative systems

Giuseppe Da Prato (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.

Asymptotic behaviour of stochastic semigroups.

Esther Dopazo (1990)

Extracta Mathematicae

The problem to be treated in this note is concerned with the asymptotic behaviour of stochastic semigroups, as the time becomes very large. The subject is largely motived by the Theory of Markov processes. Stochastic semigroups usually arise from pure probabilistic problems such as random walks stochastic differential equations and many others.An outline of the paper is as follows. Section one deals with the basic definitions relative to K-positivity and stochastic semigroups. Asymptotic behaviour...

Asymptotic estimates for a perturbation of the linearization of an equation for compressible viscous fluid flow

Gerhard Ströhmer (2008)

Studia Mathematica

We prove a priori estimates for a linear system of partial differential equations originating from the equations for the flow of a barotropic compressible viscous fluid under the influence of the gravity it generates. These estimates will be used in a forthcoming paper to prove the nonlinear stability of the motionless, spherically symmetric equilibrium states of barotropic, self-gravitating viscous fluids with respect to perturbations of zero total angular momentum. These equilibrium states as...

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