相关论文: An asymptotic preserving scheme for a tumor growth…

In this paper, we investigate a class of tumor growth models governed by porous medium-type equations with uncertainties arisen from the growth function, initial condition, tumor support radius or other parameters in the model. We develop a…

This paper studies asymptotic behavior of solutions of a free boundary problem modeling the growth of tumors with two species of cells: proliferating cells and quiecent cells. In previous literatures it has been proved that this problem has…

In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…

In this work, we design and analyze an asymptotic preserving (AP), semi-implicit finite volume scheme for the scaled compressible isentropic Euler system with a singular pressure law known as the congestion pressure law. The congestion…

We consider a (degenerate) cross-diffusion model of tumor growth structured by phenotypic trait. We prove the existence of weak solutions and the incompressible limit as the pressure becomes stiff extending methods recently introduced in…

We investigate the linear stability analysis of a pathway-based diffusion model (PBDM), which characterizes the dynamics of the engineered Escherichia coli populations [X. Xue and C. Xue and M. Tang, P LoS Computational Biology, 14 (2018),…

We consider a macroscopic model for the dynamics of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Given a power-law constitutive relation between the pressure and cell density, the model can be…

In this paper we study a tumor growth model with nutrients. The model presents dynamic patch solutions due to the contact inhibition among the tumor cells. We show that when the nutrients do not diffuse and the cells do not die, the tumor…

We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when the pressure-density relationship becomes highly nonlinear.…

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…

We investigate the general Porous Medium Equations with drift and source terms that model tumor growth. Incompressible limit of such models has been well-studied in the literature, where convergence of the density and pressure variables are…

We introduce and study a notion of Asymptotic Preserving schemes, related to convergence in distribution, for a class of slow-fast Stochastic Differential Equations. In some examples, crude schemes fail to capture the correct limiting…

We investigate avascular tumour growth as a two-phase process consisting of cells and liquid. Based on the one-dimensional continuum moving-boundary model formulated by (Byrne, King, McElwain, Preziosi, Applied Mathematics Letters, 2003,…

We study a free boundary problem modelling the growth of non-necrotic tumors with fluid-like tissues. The fluid velocity satisfies Stokes equations with a source determined by the proliferation rate of tumor cells which depends on 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…

In this work we study a tissue growth model with applications to tumour growth. The model is based on that of Perthame, Quir\'os, and V\'azquez proposed in 2014 but incorporates the advective effects caused, for instance, by the presence of…

In this paper, we prove the asymptotic stability of the incompressible porous media (IPM) equation near a stable stratified density, for initial perturbations in the Sobolev space $H^k$ with any $2<k \in\mathbb{R}$. While it is known that…

For tumor growth, the morphological instability provides a mechanism for invasion via tumor fingering and fragmentation. This work considers the asymptotic stability of a free boundary tumor model with a periodic supply of external…

An asymptotic preserving and energy stable scheme for the barotropic Euler system under the low Mach number scaling is designed and analysed. A velocity shift proportional to the pressure gradient is introduced in the convective fluxes,…

We propose a new pressure-based structure-preserving (SP) and quasi asymptotic preserving (AP) staggered semi-implicit finite volume scheme for the unified first order hyperbolic formulation of continuum mechanics. The unified model is…