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… 

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

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

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

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

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

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

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

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

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

Time discretization of a nonlinear phase field system in general domains

TLDR
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 £Omega $\end{document} is a bounded domain, but for unbounded domains the analysis of the system seems to be at an early stage.

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

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

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

References

SHOWING 1-10 OF 21 REFERENCES

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

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

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

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

Frost propagation in wet porous media

A water saturated porous medium freezes when it is chilled. The frost line which separates the frozen part and the unfrozen part is a free surface. Experiments show that a depression pppears on the

Non-Smooth Thermomechanics

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

ON UNDAMPED HEAT WAVES IN AN ELASTIC SOLID

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

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,

A re-examination of the basic postulates of thermomechanics

  • A. GreenP. M. Naghdi
  • 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.

A new thermoviscous theory for fluids

Thermoelasticity without energy dissipation

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