相关论文: Well-posedness and Long-time Behavior of a Bulk-su…

We propose and investigate a model for lipid raft formation and dynamics in biological membranes. The model describes the lipid composition of the membrane and an interaction with cholesterol. To account for cholesterol exchange between…

We study the long-time dynamics of a bulk-surface convective Cahn--Hilliard system describing phase separation processes with bulk-surface interaction. The presence of convection terms leads to a non-autonomous dynamical system and prevents…

We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows with chemotaxis effect. The PDE system couples a Navier-Stokes equation for the fluid velocity, a convective Cahn-Hilliard equation for the…

In this paper, we study a hydrodynamic phase-field system modeling the deformation of functionalized membranes in incompressible viscous fluids. The governing PDE system consists of the Navier-Stokes equations coupled with a convective…

We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…

We consider an evolutionary PDE system coupling the Cahn-Hilliard equation with singular potential, mass source and transport effects, to a Brinkman-type relation for the macroscopic velocity field and to a further equation describing the…

In this work, we analytically investigate a degenerating PDE system for phase separation and complete damage processes considered on a nonsmooth time-dependent domain with mixed boundary conditions. The evolution of the system is described…

We consider a general class of bulk-surface convective Cahn--Hilliard systems with dynamic boundary conditions. In contrast to classical Neumann boundary conditions, the dynamic boundary conditions of Cahn--Hilliard type allow for dynamic…

This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…

We consider a class of bulk-surface coupled Cahn-Hilliard systems in a smooth, bounded domain $\Omega\subset\mathbb{R}^{d}$ $(d\in\{2,3\})$, where the trace value of the bulk phase variable is connected to the surface phase variable via a…

We examine a thermodynamically consistent diffuse interface model for bulk-surface viscous fluid mixtures. This model consists of a Navier--Stokes--Cahn--Hilliard model in the bulk coupled to a surface Navier--Stokes--Cahn--Hilliard system…

We study the well-posedness of a modified degenerate Cahn-Hilliard type model for surface diffusion. With degenerate phase-dependent diffusion mobility and additional stabilizing function, this model is able to give the correct sharp…

We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous…

The formal sharp-interface asymptotics in a degenerate Cahn-Hilliard model for viscoelastic phase separation with cross-diffusive coupling to a bulk stress variable are shown to lead to non-local lower-order counterparts of the classical…

We recover the so-called field-road diffusion model as the hydrodynamic limit of an interacting particle system. The former consists of two parabolic PDEs posed on two sets of different dimensions (a "field" and a "road" in a population…

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 consider a mathematical model for heterogeneous catalysis in a finite three-dimensional pore of cylinder-like geometry, with the lateral walls acting as a catalytic surface. The system under consideration consists of a…

The Cahn--Hilliard equation is one of the most common models to describe phase segregation processes in binary mixtures. In recent times, various dynamic boundary conditions have been introduced to model interactions of the materials with…

We analyze a diffuse interface model that couples a viscous Cahn-Hilliard equation for the phase variable with a diffusion-reaction equation for the nutrient concentration. The system under consideration also takes into account some…

A system with equation and dynamic boundary condition of Cahn-Hilliard type is considered. This system comes from a derivation performed in Liu-Wu (Arch. Ration. Mech. Anal. 233 (2019), 167--247) via an energetic variational approach.…