# Solvability and asymptotic analysis of a generalization of the Caginalp phase field system

@article{Canevari2011SolvabilityAA, title={Solvability and asymptotic analysis of a generalization of the Caginalp phase field system}, author={Giacomo Canevari and Pierluigi Colli}, journal={arXiv: Analysis of PDEs}, year={2011} }

We study a diffusion model of phase field type, which consists of a system of two partial differential equations involving as variables the thermal displacement, that is basically the time integration of temperature, and the order parameter. Our analysis covers the case of a non-smooth (maximal monotone) graph along with a smooth anti-monotone function in the phase equation. Thus, the system turns out a generalization of the well-known Caginalp phase field model for phase transitions when…

## 12 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…

### A P ] 2 8 M ay 2 01 2 Convergence properties for a generalization of the Caginalp phase field system ∗ Giacomo Canevari and Pierluigi Colli

- Mathematics
- 2014

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…

### Optimal control of a nonconserved phase field model of Caginalp type with thermal memory and double obstacle potential

- Mathematics
- 2022

In this paper, we investigate optimal control problems for a nonlinear state system which constitutes a version of the Caginalp phase ﬁeld system modeling nonisothermal phase transitions with a…

### 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…

### Global existence for a phase separation system deduced from the entropy balance

- MathematicsNonlinear Analysis
- 2020

### On a Cahn-Hilliard system with source term and thermal memory

- Mathematics
- 2022

A nonisothermal phase ﬁeld system of Cahn–Hilliard type is introduced and analyzed mathematically. The system constitutes an extension of the classical Caginalp model for nonisothermal phase…

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

- MathematicsApplied Mathematics & Optimization
- 2020

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…

### Temperature dependent extensions of the Cahn-Hilliard equation

- Mathematics
- 2021

The Cahn–Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In this paper we focus on the dynamics of these binary media, when the underlying…

### Existence for a Singular Nonlocal Phase Field System with Inertial Term

- MathematicsActa Applicandae Mathematicae
- 2022

In this paper we deal with a singular nonlocal phase field system with inertial term. The system has the logarithm of the absolute temperature θ under time derivative. Although the system has a…

### 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.

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