相关论文: Asymptotic stability for a free boundary tumor mod…

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…

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 we study a free boundary problem modeling the growth of solid tumor spheroid. It consists of two elliptic equations describing nutrient diffusion and pressure distribution within tumor, respectively. The new feature is that…

In this paper, we consider a 3-dimensional free boundary problem modeling tumor growth with the Robin boundary condition. The system involves a positive parameter $\mu$ which reflects the intensity of tumor aggressiveness. Huang, Zhang and…

In this paper, we present a rigorous mathematical analysis of a free boundary problem modeling the growth of a vascular solid tumor with a necrotic core. If the vascular system supplies the nutrient concentration $\sigma$ to the tumor at a…

This paper is concerned with a multi-dimensional free boundary problem modeling the growth of a tumor with two species of cells: proliferating cells and quiescent cells. This free boundary problem has a unique radial stationary solution. By…

This paper is concerned with a nonlinear free boundary problem modeling the growth of spherically symmetric tumors with angiogenesis, set with a Robin boundary condition. In which, both nonnecrotic tumors and necrotic tumors are taken into…

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…

We study a free boundary problem modeling multi-layer tumor growth with a small time delay $\tau$, representing the time needed for the cell to complete the replication process. The model consists of two elliptic equations which describe…

In this paper we study asymptotic behavior of solutions for a free boundary problem modeling the growth of tumors containing two species of cells: proliferating cells and quiescent cells. This tumor model was proposed by Pettet et al in…

In this paper we study a nonlinear free boundary problem on the radial growth of a two-layer solid tumor with a quiescent core. The tumor surface and its inner interface separating the proliferating cells and the quiescent cells are both…

We study a free boundary problem modeling tumor growth with a T-periodic supply $\Phi(t)$ of external nutrients. The model contains two parameters $\mu$ and $\widetilde{\sigma}$. We first show that (i) zero radially symmetric solution is…

In this paper we study a free boundary problem for the growth of multi-layer tumors in necrotic phase. The tumor region is strip-like and divided into necrotic region and proliferating region with two free boundaries. The upper free…

In this paper we deal with a free boundary problem modeling the growth of nonnecrotic tumors.The tumor is treated as an incompressible fluid, the tissue elasticity is neglected and no chemical inhibitor species are present. We re-express…

In this paper we study asymptotic behavior of solutions for a multidimensional free boundary problem modelling the growth of nonnecrotic tumors. We first establish a general result for differential equations in Banach spaces possessing a…

In this paper, we study a nonlinear free boundary problem modeling the growth of spherically symmetric tumors. The tumor consists of a central necrotic core, an intermediate annual quiescent-cell layer, and an outer proliferating-cell…

In this paper, we consider a model with tumor microenvironment involving nutrient density, extracellular matrix and matrix-degrading enzymes, which satisfy a coupled system of PDEs with a free boundary. For this coupled parabolic-hyperbolic…

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 consider a free boundary tumor model under the presence of angiogenesis and time delays in the process of proliferation, in which the cell location is incorporated. It is assumed that the tumor attracts blood vessels at a rate…