相关论文: A generalized Cahn-Hilliard equation for biologica…
Continuum mathematical models for collective cell motion normally involve reaction-diffusion equations, such as the Fisher-KPP equation, with a linear diffusion term to describe cell motility and a logistic term to describe cell…
The degenerate Cahn-Hilliard equation is a standard model to describe living tissues. It takes into account cell populations undergoing short-range attraction and long-range repulsion effects. In this framework, we consider the usual…
In this work, we consider a diffuse interface model for tumour growth in the presence of a nutrient which is consumed by the tumour. The system of equations consists of a Cahn--Hilliard equation with source terms for the tumour cells and a…
We present a stochastic model which describes fronts of cells invading a wound. In the model cells can move, proliferate, and experience cell-cell adhesion. We find several qualitatively different regimes of front motion and analyze the…
We consider a diffuse interface model for tumour growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation. The coupled system of partial differential equations models a tumour growing in the…
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…
We present a discrete stochastic model which represents many of the salient features of the biological process of wound healing. The model describes fronts of cells invading a wound. We have numerical results in one and two dimensions. In…
We consider a mathematical model coupling the Cahn-Hilliard system for phase separation with an additional equation describing the diffusion process of a chemical quantity whose concentration influences the physical process. The main…
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…
We consider a diffuse interface model for tumor growth consisting of a Cahn--Hilliard equation with source terms coupled to a reaction-diffusion equation, which models a tumor growing in the presence of a nutrient species and surrounded by…
In this paper, we study a system of three evolutionary operator equations involving fractional powers of selfadjoint, monotone, unbounded, linear operators having compact resolvents. This system constitutes a generalization of a phase field…
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 Cahn-Hilliard-Biot model with respect to its mathematical well-posedness. The system models flow through deformable porous media in which the solid material has two phases with distinct material properties. The two phases of…
The Cahn-Hilliard equation is one of the most common models to describe phase separation processes in mixtures of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic…
The Cahn-Hilliard model with reaction terms can lead to situations in which no coarsening is taking place and, in contrast, growth and division of droplets occur which all do not grow larger than a certain size. This phenomenon has been…
In this paper, we study a generalized Camassa-Holm (gCH) model with both dissipation and dispersion, which has (N + 1)-order nonlinearities and includes the following three integrable equations: the Camassa-Holm, the Degasperis-Procesi, and…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
Mechanical effects have mostly been neglected so far in phase field tumour models that are based on a Cahn-Hilliard approach. In this paper we study a macroscopic mechanical model for tumour growth in which cell-cell adhesion effects are…
We formulate a Hele-Shaw type free boundary problem for a tumor growing under the combined effects of pressure forces, cell multiplication and active motion, the latter being the novelty of the present paper. This new ingredient is…
We investigate a multiphase Cahn-Hilliard model for tumor growth with general source terms. The multiphase approach allows us to consider multiple cell types and multiple chemical species (oxygen and/or nutrients) that are consumed by the…