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Displaying similar documents to “Nonlinear systems of parabolic PDE's for phase change problem”

On the unique solvability of a nonlocal phase separation problem for multicomponent systems

Jens A. Griepentrog (2004)

Banach Center Publications

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A nonlocal model of phase separation in multicomponent systems is presented. It is derived from conservation principles and minimization of free energy containing a nonlocal part due to particle interaction. In contrast to the classical Cahn-Hilliard theory with higher order terms this leads to an evolution system of second order parabolic equations for the particle densities, coupled by nonlinear and nonlocal drift terms, and state equations which involve both chemical and interaction...

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.

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...

Introduction to the models of phase transitions

A. Visintin (1998)

Bollettino dell'Unione Matematica Italiana

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Le transizioni di fase si presentano in svariati processi fisici: un esempio tipico è la transizione solido-liquido. Il classico modello matematico, noto come , tiene conto solo dello scambio del calore latente e della diffusione termica nelle fasi. Si tratta di un problema di frontiera libera, poiché l'evoluzione dell'interfaccia solido liquido è una delle incognite. In questo articolo si rivedono le formulazioni forte e debole di tale problema, e quindi si considerano alcune generalizzazioni...