相关论文: Existence analysis for a reaction-diffusion Cahn-H…

The global-in-time existence of weak solutions to a degenerate Cahn-Hilliard cross-diffusion system with singular potential in a bounded domain with no-flux boundary conditions is proved. The model consists of two coupled parabolic…

The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…

We analyze the mathematical properties of a multi-species biofilm cross-diffusion model together with very general reaction terms and mixed Dirichlet-Neumann boundary conditions on a bounded domain. This model belongs to the class of…

A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a…

We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…

We study a nonlocal Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects and degenerate mobility. The nonlocality is described by means of a symmetric singular kernel. We define a notion of weak solution adapted to…

We study the existence of weak solutions to a Cahn--Hilliard--Darcy system coupled with a convection-reaction-diffusion equation through the fluxes, through the source terms and in Darcy's law. The system of equations arises from a mixture…

We study a phase field model proposed recently in the context of tumour growth. The model couples a Cahn-Hilliard-Brinkman (CHB) system with a elliptic reaction-diffusion equation for a nutrient. The fluid velocity, governed by the Brinkman…

The existence of global weak solutions to a parabolic energy-transport system in a bounded domain with no-flux boundary conditions is proved. The model can be derived in the diffusion limit from a kinetic equation with a linear collision…

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 consider a phase-field system modelling solid tumour growth. This system consists of a Cahn-Hilliard equation coupled with a nutrient equation. The former is characterised by a degenerate mobility and a singular potential. Both equations…

The continuous dependence on the initial data and consequently the uniqueness of bounded weak solutions to a class of triangular reaction-cross-diffusion equations is shown. The class includes two-species doubly degenerate equations for…

Several problems, issued from physics, biology or the medical science, lead to parabolic equations set in two sub-domains separated by a membrane with selective permeability to specific molecules. The corresponding boundary conditions,…

We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows influenced by interactions with a soluble chemical substance, encompassing the chemotaxis effect, mass transport, and reactions. In the…

In this work, we study a model consisting of a Cahn-Hilliard-type equation for the concentration of tumour cells coupled to a reaction-diffusion type equation for the nutrient density and a Brinkman-type equation for the velocity. We equip…

We consider a diffuse-interface model for two-phase incompressible viscous flows with a soluble surfactant in a bounded porous medium. This hydrodynamic system consists of a Darcy--Forchheimer equation for the seepage velocity…

We analyze a phase field model for tumor growth consisting of a Cahn-Hilliard-Brinkman system, ruling the evolution of the tumor mass, coupled with an advection-reaction-diffusion equation for a chemical species acting as a nutrient. The…

Existence and uniqueness are investigated 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…

A multidimensional model of biofilm growth present in the supernatant water of a Slow Sand Filter is derived. The multiphase model, consisting of solid and liquid phases, is written as a convection-reaction system with a Cahn-Hilliard-type…

We prove global existence and uniqueness of solutions to a Cahn-Hilliard system with nonlinear viscosity terms and nonlinear dynamic boundary conditions. The problem is highly nonlinear, characterized by four nonlinearities and two separate…