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

Zhu, Peicheng

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Displaying similar documents to “Viscosity solutions to a new phase-field model for martensitic phase transformations”

A model of cardiac tissue as an excitable medium with two interacting pacemakers having refractory time

Alexander Loskutov, Sergei Rybalko, Ekaterina Zhuchkova (2003)

Banach Center Publications

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A quite general model of the nonlinear interaction of two impulse systems describing some types of cardiac arrhythmias is developed. Taking into account a refractory time the phase locking phenomena are investigated. Effects of the tongue splitting and their interweaving in the parametric space are found. The results obtained allow us to predict the behavior of excitable systems with two pacemakers depending on the type and intensity of their interaction and the initial phase. ...

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...

Global existence of weak solutions to the Fried-Gurtin model of phase transitions

Zenon Kosowski (2007)

Applicationes Mathematicae

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We prove the existence of global in time weak solutions to a three-dimensional system of equations arising in a simple version of the Fried-Gurtin model for the isothermal phase transition in solids. In this model the phase is characterized by an order parameter. The problem considered here has the form of a coupled system of three-dimensional elasticity and parabolic equations. The system is studied with the help of the Faedo-Galerkin method using energy estimates.

Nonlinear systems of parabolic PDE's for phase change problem

Kenmochi, Nobuyuki

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Non-standard applications of the Łojasiewicz-Simon theory: Stabilization to equilibria of solutions to phase-field models

Eduard Feireisl, Hana Petzeltová (2008)

Banach Center Publications

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This is a survey of results on the long-time behavior of solutions to phase-field models and related problems. The central idea is based on several non-standard applications of the Łojasiewicz-Simon theory.

Unique global solvability of 1D Fried-Gurtin model

Zenon Kosowski (2007)

Applicationes Mathematicae

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We investigate a 1-dimensional simple version of the Fried-Gurtin 3-dimensional model of isothermal phase transitions in solids. The model uses an order parameter to study solid-solid phase transitions. The free energy density has the Landau-Ginzburg form and depends on a strain, an order parameter and its gradient. The problem considered here has the form of a coupled system of one-dimensional elasticity and a relaxation law for a scalar order parameter. Under some physically justified...

Computational studies of anisotropic diffuse interface model of microstructure formation in solidification

Beneš, Michal

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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.

Global existence for the conserved phase field model with memory and quadratic nonlinearity.

Colli, P., Gilardi, G., Grasselli, M., Schimperna, G. (2001)

Portugaliae Mathematica. Nova Série

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On a phase transition model of Penrose-Fife type

Gianni Gilardi (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We deal with a Penrose-Fife type model for phase transition. We assume a rather general constitutive low for the heat flux and treat the Dirichlet and Neumann boundary condition for the temperature. Some of our proofs apply to different types of boundary conditions as well and improve some results existing in the literature.