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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…

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…

If a differential equation in a Banach manifold is invariant or quasi-invariant under the action of one or more Lie groups, then its stationary points cannot be isolated, so that classical linearized stability theorem does not apply to it.…

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…

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 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…

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…

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…

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 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 a free boundary problem modeling solid tumor growth with vasculature which supplies nutrients to the tumor; this is characterized in the Robin boundary condition. It was recently established [Discrete Cont. Dyn.…

The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium.…

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…

In this paper we make rigorous mathematical analysis to a free boundary problem modeling the growth of necrotic tumors. A remarkable feature of this free boundary problem is that it contains two different-type free surfaces: One is the…

A two-dimensional free boundary model for the growth of multi-layer tumors has been proposed in [S. Cui, J. Escher: ARMA 191 (2009) 173-193] where the authors derive well-posedness in a functional analytic setting, the stationary solutions…

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…

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 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 study a linearized eigenvalue problem derived from a a free boundary problem modeling the growth of a tumor containing two species of cells: proliferating cells and quiescent cells. The reduced form of this eigenvalue…

Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…