# 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}
}
• Published 20 July 2011
• Mathematics
• arXiv: Analysis of PDEs
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…

### 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

### 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

• Mathematics
Applied 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

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, Mathematics
Communications 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.

## References

SHOWING 1-10 OF 22 REFERENCES

### Well-posedness of the weak formulation for the phase-field model with memory

• Mathematics
• 1997
A phase–field model based on the Gurtin–Pipkin heat flux law is considered. This model consists in a Volterra integrodifferential equation of hyperbolic type coupled with a nonlinear parabolic

### ON UNDAMPED HEAT WAVES IN AN ELASTIC SOLID

• Engineering
• 1992
This paper is concerned with thermoelastic material behavior whose constitutive response functions possess thermal features that are more general than in the usual classical thermoelasticity. After a

### A re-examination of the basic postulates of thermomechanics

• Engineering
Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
• 1991
This paper is mainly concerned with a re-examination of the basic postulates and the consequent procedure for the construction of the constitutive equations of material behaviour in thermomechanics.

### Linear and Quasilinear Equations of Parabolic Type

linear and quasi linear equations of parabolic type by o a ladyzhenskaia 1968 american mathematical society edition in english, note citations are based on reference standards however formatting

### Thermoelasticity without energy dissipation

• Engineering
• 1993
This paper deals with thermoelastic material behavior without energy dissipation; it deals with both nonlinear and linear theories, although emphasis is placed on the latter. In particular, the

### Non-Smooth Thermomechanics

• Mathematics
• 2001
1. The Description of a Material.- 3. The Constitutive Laws. Case of No Constraint on the State Quantities or Their Velocities.- 5. The Constitutive Laws on a Discontinuity Surface.- 6. Deformable

### Compact sets in the spaceLp(O,T; B)

SummaryA characterization of compact sets in Lp (0, T; B) is given, where 1⩽P⩾∞ and B is a Banach space. For the existence of solutions in nonlinear boundary value problems by the compactness method,