相关论文: Analysis of a nonisothermal and conserved phase fi…

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 transitions with a conserved order parameter. It…

We consider a non-isothermal modified Cahn--Hilliard equation which was previously analyzed by M. Grasselli et al. Such an equation is characterized by an inertial term and a viscous term and it is coupled with a hyperbolic heat equation.…

In this note, we study the optimal control of a nonisothermal phase field system of Cahn-Hilliard type that constitutes an extension of the classical Caginalp model for nonisothermal phase transitions with a conserved order parameter. The…

In this note, we study the optimal control of a nonisothermal phase field system of Cahn-Hilliard type that constitutes an extension of the classical Caginalp model for nonisothermal phase transitions with a conserved order parameter. It…

We consider a differential model describing nonisothermal fast phase separation processes taking place in a three-dimensional bounded domain. This model consists of a viscous Cahn-Hilliard equation characterized by the presence of an…

This paper is concerned with a diffusion model of phase-field type, consisting of a parabolic system of two partial differential equations, interpreted as balances of microforces and microenergy, for two unknowns: the problem's order…

P. Galenko et al. proposed a modified Cahn-Hilliard equation to model rapid spinodal decomposition in non-equilibrium phase separation processes. This equation contains an inertial term which causes the loss of any regularizing effect on…

An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions.…

We study a system describing the dynamics of a two-phase flow of incompressible viscous fluids influenced by the convective heat transfer of Caginalp-type. The separation of the fluids is expressed by the order parameter which is of diffuse…

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…

We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a…

This work explores the solvability of a sixth-order Cahn--Hilliard equation with an inertial term, which serves as a relaxation of a higher-order variant of the classical Cahn--Hilliard equation. The equation includes a source term that…

A common paradigm in phase-field models with singular potentials is that global-in-time weak solutions converge to a single equilibrium only after undergoing asymptotic regularization. However, in arXiv:2510.17296 we introduced a novel…

We propose a new class of phase field models coupled to viscoelasticity with large deformations, obtained from a diffuse interface mixture model composed by a phase with elastic properties and a liquid phase. The model is formulated in the…

In this paper we deal with a singular nonlocal phase field system with inertial term. The system has the logarithm of the absolute temperature $\theta$ under time derivative. Although the system has a difficult mathematical point caused by…

Isothermal compressible two-phase flows with and without phase transition are modeled, employing Darcy's and/or Forchheimer's law for the velocity field. It is shown that the resulting systems are thermodynamically consistent in the sense…

Phase-field models are a popular choice in computational physics to describe complex dynamics of substances with multiple phases and are widely used in various applications. We present nonlocal non-isothermal phase-field models of…

Phase field models are widely used to describe multiphase systems. Here a smooth indicator function, called phase field, is used to describe the spatial distribution of the phases under investigation. Material properties like density or…

This paper is concerned with a non-isothermal Cahn-Hilliard model based on a microforce balance. The model was derived by A. Miranville and G. Schimperna starting from the two fundamental laws of Thermodynamics, following M. Gurtin's…

A Cahn-Hilliard-Allen-Cahn phase-field model coupled with a heat transfer equation, particularly with full non-diagonal mobility matrices, is studied. After reformulating the problem w.r.t. the inverse of temperature, we proposed and…