Displaying similar documents to “Non-standard applications of the Łojasiewicz-Simon theory: Stabilization to equilibria of solutions to phase-field models”

A class of time discrete schemes for a phase–field system of Penrose–Fife type

Olaf Klein (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, a phase field system of Penrose–Fife type with non–conserved order parameter is considered. A class of time–discrete schemes for an initial–boundary value problem for this phase–field system is presented. In three space dimensions, convergence is proved and an error estimate linear with respect to the time–step size is derived.

A thermodynamic approach to nonisothermal phase-field models

Irena Pawłow (2015)

Applicationes Mathematicae

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The goal of this paper is to work out a thermodynamical setting for nonisothermal phase-field models with conserved and nonconserved order parameters in thermoelastic materials. Our approach consists in exploiting the second law of thermodynamics in the form of the entropy principle according to I. Müller and I. S. Liu, which leads to the evaluation of the entropy inequality with multipliers. As the main result we obtain a general scheme of phase-field models which...

Viscosity solutions to a new phase-field model for martensitic phase transformations

Zhu, Peicheng

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We investigate a new phase-field model which describes martensitic phase transitions, driven by material forces, in solid materials, e.g., shape memory alloys. This model is a nonlinear degenerate parabolic equation of second order, its principal part is not in divergence form in multi-dimensional case. We prove the existence of viscosity solutions to an initial-boundary value problem for this model.

Hysteresis operators in phase-field models of Penrose-fife type

Pavel Krejčí, Jürgen Sprekels (1998)

Applications of Mathematics

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Phase-field systems as mathematical models for phase transitions have drawn a considerable attention in recent years. However, while they are suitable for capturing many of the experimentally observed phenomena, they are only of restricted value in modelling hysteresis effects occurring during phase transition processes. To overcome this shortcoming of existing phase-field theories, the authors have recently proposed a new approach to phase-field models which is based on the mathematical...

Relations between constants of motion and conserved functions

Josef Janyška (2015)

Archivum Mathematicum

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We study relations between functions on the cotangent bundle of a spacetime which are constants of motion for geodesics and functions on the odd-dimensional phase space conserved by the Reeb vector fields of geometrical structures generated by the metric and an electromagnetic field.

Stabilization of walls for nano-wires of finite length

Gilles Carbou, Stéphane Labbé (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length. First we justify the model by Γ-convergence arguments. Furthermore we prove the existence of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.

Stabilization of walls for nano-wires of finite length

Gilles Carbou, Stéphane Labbé (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length. First we justify the model by Γ-convergence arguments. Furthermore we prove the existence of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.

Stabilization of walls for nano-wires of finite length

Gilles Carbou, Stéphane Labbé (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length. First we justify the model by Γ-convergence arguments. Furthermore we prove the existence of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.

Solvability of a class of phase field systems related to a sliding mode control problem

Michele Colturato (2016)

Applications of Mathematics

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We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove the existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.