相关论文: Hele-Shaw limit for a system of two reaction-(cros…

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical properties of living tissues. These two classes of models can be related using a stiff pressure law. In the incompressible…

A mathematical model for tissue growth is considered. This model describes the dynamics of the density of cells due to pressure forces and proliferation. It is known that such cell population model converges at the incompressible limit…

We study a porous medium equation that models tissue growth in a heterogeneous environment. We show that, in the incompressible limit, solutions converge to those of a weak form of a Hele-Shaw type free boundary problem. To obtain enough…

Models of tumor growth, now commonly used, present several levels of complexity, both in terms of the biomedical ingredients and the mathematical description. The simplest ones contain competition for space using purely fluid mechanical…

This paper investigates the incompressible limit of a system modelling the growth of two cells population. The model describes the dynamics of cell densities, driven by pressure exclusion and cell proliferation. It has been shown that…

In this paper we study a cross-diffusion system whose coefficient matrix is non-symmetric and degenerate. The system arises in the study of tissue growth with autophagy. The existence of a weak solution is established. We also investigate…

We study the incompressible limit of the porous medium equation with a right hand side representing either a source or a sink term, and an injection boundary condition. This model can be seen as a simplified description of non-monotone…

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…

In this paper we study the "stiff pressure limit" of the porous medium equation, where the initial density is a bounded, integrable function with a sufficient decay at infinity. Our particular model, introduced by Perthame-Quiros-Vazquez,…

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…

We study the "stiff pressure limit" of a nonlinear drift-diffusion equation, where the density is constrained to stay below the maximal value one. The challenge lies in the presence of a drift and the consequent lack of monotonicity in…

The porous medium type reaction-diffusion equation and the Hele-Shaw problem are two free boundary problems linked through the incompressible (Hele-Shaw) limit. We investigate and compare the sharp power concavities of the pressures on…

Reaction cross diffusion systems are a two species generalization of the porous media equation. These systems play an important role in the mechanical modeling of living tissues and tumor growth. Due to their mixed parabolic-hyperbolic…

This paper proposes a model for the growth two interacting populations of cells that do not mix. The dynamics is driven by pressure and cohesion forces on the one hand and proliferation on the other hand. Following earlier works on the…

We present a two-species model with applications in tumour modelling. The main novelty is the coupling of both species through the so-called Brinkman law which is typically used in the context of visco-elastic media, where the velocity…

The mathematical modeling of tumor growth leads to singular stiff pressure law limits for porous medium equations with a source term. Such asymptotic problems give rise to free boundaries, which, in the absence of active motion, are…

This paper proposes a new approach to solving the Buckley-Leverett System, which is to consider a compressible approximation model characterized by a stiff pressure law. Passing to the incompressible limit, the compressible model gives rise…

We formulate a Hele-Shaw type free boundary problem for a tumor growing under the combined effects of pressure forces, cell multiplication and active motion, the latter being the novelty of the present paper. This new ingredient is…

We consider weak solutions to a problem modeling tumor growth. Under certain conditions on the initial data, solutions can be obtained by passing to the stiff (incompressible) limit in a porous medium type problem with a Lotka-Volterra…

We analyze a system of cross-diffusion equations that models the growth of an avascular-tumor spheroid. The model incorporates two nonlinear diffusion effects, degeneracy type and super diffusion. We prove the global existence of weak…