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Related papers: Asymptotic behavior of a nonisothermal viscous Cah…

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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.…

Analysis of PDEs · Mathematics 2013-10-04 Cecilia Cavaterra , Maurizio Grasselli , Hao Wu

In this paper, we study the longtime asymptotic behavior of a phase separation process occurring in a three-dimensional domain containing a fluid flow of given velocity. This process is modeled by a viscous convective Cahn-Hilliard system,…

Analysis of PDEs · Mathematics 2018-03-13 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

This paper deals with a conserved phase field system that couples the energy balance equation with a Cahn--Hilliard type system including temperature and the inertial term for the order parameter. In the case without inertial term, the…

Analysis of PDEs · Mathematics 2025-05-28 Pierluigi Colli , Shunsuke Kurima

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…

Analysis of PDEs · Mathematics 2011-09-16 Pierluigi Colli , Gianni Gilardi , Paolo Podio-Guidugli , Jürgen Sprekels

We investigate the Cahn-Hilliard equation with nonlinear diffusion and non-degenerate mobility modeling phase separation phenomena in complex systems (e.g., crystals and polymers). Previous results in the literature on this model relied on…

Analysis of PDEs · Mathematics 2025-10-10 Monica Conti , Stefania Gatti , Andrea Giorgini , Giulio Schimperna

We consider a class of Cahn-Hilliard equation that characterizes phase separation phenomena of binary mixtures in a bounded domain $\Omega \subset \mathbb{R}^d$ $(d\in \{2,3\})$ with non-permeable boundary. The equations in the bulk are…

Analysis of PDEs · Mathematics 2024-06-03 Maoyin Lv , Hao Wu

We introduce a nonisothermal phase-field system of Caginalp type that describes tumor growth under hyperthermia. The model couples a possibly viscous Cahn-Hilliard equation, governing the evolution of the healthy and tumor phases, with an…

Analysis of PDEs · Mathematics 2025-10-13 Giulia Cavalleri , Pierluigi Colli , Elisabetta Rocca

An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward…

Analysis of PDEs · Mathematics 2021-06-03 Pierluigi Colli , Takeshi Fukao , Luca Scarpa

In this paper, we study initial-boundary value problems for the Cahn--Hilliard system with convection and nonconvex potential, where dynamic boundary conditions are assumed for both the associated order parameter and the corresponding…

Optimization and Control · Mathematics 2018-03-15 Gianni Gilardi , Jürgen Sprekels

In this paper, we prove the existence and global boundedness from above for a solution to an integrodifferential model for nonisothermal multi-phase transitions under nonhomogeneous third type boundary conditions. The system couples a…

Analysis of PDEs · Mathematics 2015-03-17 Pierluigi Colli , Pavel Krejčí , Elisabetta Rocca , Jürgen Sprekels

We consider a class of nonlocal Cahn-Hilliard equations in a bounded domain $\Omega\subset\mathbb{R}^{d}$ $(d\in\{2,3\})$, subject to a nonlocal kinetic rate dependent dynamic boundary condition. This diffuse interface model describes phase…

Analysis of PDEs · Mathematics 2024-12-11 Maoyin Lv , Hao Wu

We consider a Cahn-Hilliard equation which is the conserved gradient flow of a nonlocal total free energy functional. This functional is characterized by a Helmholtz free energy density, which can be of logarithmic type. Moreover, the…

Analysis of PDEs · Mathematics 2013-11-15 Helmut Abels , Stefano Bosia , Maurizio Grasselli

This note is concerned with a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by boundary and initial conditions. The system arises from a model of…

Analysis of PDEs · Mathematics 2017-02-03 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

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.…

Analysis of PDEs · Mathematics 2012-02-24 Pierluigi Colli , Gianni Gilardi , Paolo Podio-Guidugli , Jürgen Sprekels

In this paper, we study a hyperbolic relaxation of the viscous Cahn--Hilliard system with zero Neumann boundary conditions. In fact, we consider a relaxation term involving the second time derivative of the chemical potential in the first…

Analysis of PDEs · Mathematics 2024-10-15 Pierluigi Colli , Jürgen Sprekels

The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range…

Analysis of PDEs · Mathematics 2023-07-28 Chun Liu , Hao Wu

We study a nonlinear coupled system of partial differential equations arising from thermo--reaction--phase models. The system combines a heat diffusion equation, temperature-dependent chemical reactions of Arrhenius type, and a phase…

Analysis of PDEs · Mathematics 2026-04-24 Gossrin Jean-Marc Bomisso , Ali Ouattara Kouma , Marie Esther Anassé

In this paper we propose a mathematical model of phase separation for a quasi-incompressible binary mixture where the spinodal decomposition is induced by an heat flux governed by the Cattaneo-Maxwell equation. As usual, the phase…

Mathematical Physics · Physics 2013-06-04 A. Berti , I. Bochicchio , M. Fabrizio

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…

Analysis of PDEs · Mathematics 2011-03-24 Pierluigi Colli , Gianni Gilardi , Paolo Podio-Guidugli , Juergen Sprekels

We consider a class of Cahn-Hilliard equation that models phase separation process of binary mixtures involving nontrivial boundary interactions in a bounded domain with non-permeable wall. The system is characterized by certain dynamic…

Analysis of PDEs · Mathematics 2023-07-28 Takeshi Fukao , Hao Wu
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