相关论文: Tumor Growth with Nutrients: Regularity and Stabil…

We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a…

In this paper, a free boundary problem modelling the growth of tumor is considered. The model includes two reaction-diffusion equations modelling the diffusion of nutrient and drug in the tumor and three hyperbolic equations describing the…

A general model for the ontogenetic growth of living organisms has been recently proposed. Here we investigate the extension of this model to the growth of solid malignant tumors. A variety of in vitro and in vivo data are analyzed and…

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…

We study a tumor growth model in two space dimensions, where proliferation of the tumor cells leads to expansion of the tumor domain and migration of surrounding normal tissues into the exterior vacuum. The model features two moving…

In this paper we study a mathematical model for the growth of nonnecrotic solid tumor. The tumor is assumed to be radially symmetric and its radius R(t) is an unknown function of time t as tumor growth, and the model is in the form of a…

We derive a Cahn-Hilliard-Darcy model to describe multiphase tumour growth taking interactions with multiple chemical species into account as well as the simultaneous occurrence of proliferating, quiescent and necrotic regions. Via a…

We studied the effect of additive and multiplicative noises on the growth of a tumor based on a logistic growth model. The steady-state probability distribution and the average population of the tumor cells were given to explain the…

The influence of random fluctuations on the recruitment of effector cells towards a tumor is studied by means of a stochastic mathematical model. Aggressively growing tumors are confronted against varying intensities of the cell-mediated…

In this manuscript, we study a nonlinear model of tumor growth, described by a coupled hyperbolic-elliptic system of partial differential equations. In this model, the compressible flow of tumor cells is modeled by a transport equation for…

We study a moving boundary problem describing the growth of nonnecrotic tumors in different regimes of vascularisation. This model consists of two decoupled Dirichlet problem, one for the rate at which nutrient is added to the tumor domain…

In this paper we propose an ecological resilience point of view on cancer. This view is based on the analysis of a simple ODE model for the interactions between cancer and normal cells. The model presents two regimes for tumor growth. In…

This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular…

Tumor cells develop different features to adapt to environmental conditions. A prominent example is the ability of tumor cells to switch between migratory and proliferative phenotypes, a phenomenon known as go-or-grow mechanism. It is…

Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a…

Radiation Therapy (XRT) is one of the most common cancer treatment methods. In this paper, a new mathematical model is proposed for the population dynamics of heterogeneous tumor cells following external beam radiation treatment. According…

We study an optimal control problem for a stochastic model of tumour growth with drug application. This model consists of three stochastic hyperbolic equations describing the evolution of tumour cells. It also includes two stochastic…

Tumour cells have to acquire a number of capabilities if a neoplasm is to become a cancer. One of these key capabilities is increased motility which is needed for invasion of other tissues and metastasis. This paper presents a qualitative…

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…

This paper aims at proving asymptotic stability of the radial stationary solution of a free boundary problem modeling the growth of nonnecrotic tumors with fluid-like tissues. In a previous paper we considered the case where the nutrient…