相关论文: An Allen-Cahn tumor growth model with temperature
Consistent perturbation theory for thermodynamical quantities in strongly type II superconductors in magnetic field at low temperatures is developed. It is complementary to the existing expansion valid at high temperatures. Magnetization…
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…
In this paper, we studied phase-space analysis of a certain mathematical model of tumor growth with an immune responses and chemotherapy therapy. Mathematical modelling of this process is viewed as a potentially powerful tool in the…
In this paper, we study an initial boundary value problem of the Cahn-Hilliard-Darcy system with a non-autonomous mass source term $S$ that models tumor growth. We first prove the existence of global weak solutions as well as the existence…
This paper proposes an explicit Fourier-Klibanov method as a new approximation technique for an age-dependent population PDE of Gompertz type in modeling the evolution of tumor density in a brain tissue. Through suitable nonlinear and…
This paper deals with a general system of equations and conditions arising from a mathematical model of prostate cancer growth with chemotherapy and antiangiogenic therapy that has been recently introduced and analyzed (see [P. Colli et…
During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time,…
In this paper we present a method for estimating unknown parameters that appear on an avascular, spheric tumour growth model. The model for the tumour is based on nutrient driven growth of a continuum of live cells, whose birth and death…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
In this paper we study nonlocal-to-local asymptotics for a tumor-growth model coupling a viscous Cahn-Hilliard equation describing the tumor proportion with a reaction-diffusion equation for the nutrient phase parameter. First, we prove…
The work presents a study of the non-linear mathematical model of tumor growth, proposed by Kolev and Zubik-Kowal (2011). The model is described by a system composed of four partial differential equations that represent the evolution of the…
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…
Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn-Hilliard equations. However, often Stokes or Brinkman flows are more appropriate flow models.…
We introduce a multi-species diffuse interface model for tumor growth, characterized by its incorporation of essential features related to chemotaxis, angiogenesis and proliferation mechanisms. We establish the weak well-posedness of the…
This paper presents a model for tumor growth using nonlocal velocity. We establish some results on the existence and uniqueness of the solution for a nonlocal tumor growth model. Many experiences show that tumor spheroid can be invariant by…
A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution…
A phase field model for tumour growth is introduced that is based on a Brinkman law for convective velocity fields. The model couples a convective Cahn-Hilliard equation for the evolution of the tumour to a reaction-diffusion-advection…
In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes chemotaxis term directed to vasculature. First, we obtain some a priori estimates for the (possible) solutions of the model. In particular,…
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…
We present a novel Ensemble Monte Carlo Growth method to sample the equilibrium thermodynamic properties of random chains. The method is based on the multicanonical technique of computing the density of states in the energy space. Such a…