# Convergence properties for a generalization of the Caginalp phase field system

@article{Canevari2013ConvergencePF, title={Convergence properties for a generalization of the Caginalp phase field system}, author={Giacomo Canevari and Pierluigi Colli}, journal={Asymptot. Anal.}, year={2013}, volume={82}, pages={139-162} }

We are concerned with a phase field system consisting of two partial differential equations in terms of the variables thermal displacement, that is basically the time integration of temperature, and phase parameter. The system is a generalization of the well-known Caginalp model for phase transitions, when including a diffusive term for the thermal displacement in the balance equation and when dealing with an arbitrary maximal monotone graph, along with a smooth anti-monotone function, in the…

## 6 Citations

Analysis and optimal control theory for a phase field model of Caginalp type with thermal memory

- Mathematics
- 2021

A nonlinear extension of the Caginalp phase field system is considered that takes thermal memory into account. The resulting model, which is a first-order approximation of a thermodynamically…

Asymptotic analyses and error estimates for a Cahn-Hilliard type phase field system modelling tumor growth

- Mathematics
- 2015

This paper is concerned with a phase field system of Cahn-Hilliard type that is related to a tumor growth model and consists of three equations in terms of the variables order parameter, chemical…

Singular limit of an integrodifferential system related to the entropy balance

- Physics
- 2013

A thermodynamic model describing phase transitions with thermal memory, in terms of an entropy equation and a momentum balance for the microforces, is adressed. Convergence results and error…

Time discretization of a nonlinear phase field system in general domains

- Computer Science, MathematicsCommunications on Pure & Applied Analysis
- 2019

It turns out that the nonlinear phase field system is a generalization of the Caginalp phase field model and it has been studied by many authors in the case that Â£Omega $\end{document} is a bounded domain, but for unbounded domains the analysis of the system seems to be at an early stage.

Sliding Mode Control for a Generalization of the Caginalp Phase-Field System

- Mathematics
- 2019

In the present paper, we present and solve the sliding mode control (SMC) problem for a second-order generalization of the Caginalp phase-field system. This generalization, inspired by the theories…

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