Both compressible and incompressible porous medium models have been used in the literature to describe the mechanical aspects of living tissues, and in particular of tumor growth. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems of Hele-Shaw type where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. Then, a coupled system of equations describes the cell density and the nutrient...
International audienceModels of tissue growth are now well established, in particular in relation to...
In this paper, we consider a multispecies variant of the porous media equation used in cancer modell...
This paper proposes a model for the growth of two interacting populations of cells that do not mix. ...
Both compressible and incompressible porous medium models have been used in the literature to descri...
Both compressible and incompressible porous medium models are used in the literature to describe the...
We study the incompressible limit for a two-species model with applications to tissue growth in the ...
We consider a cross-diffusion model of tumor growth structured by phenotypic trait. We prove the exi...
16 pagesInternational audienceVarious models of tumor growth are available in the litterature. A fir...
We study a two-species model of tissue growth describing dynamics under mechanical pressure and cell...
International audienceModels of tumor growth, now commonly used, present several levels of complexit...
International audienceA mathematical model for tissue growth is considered. This model describes the...
International audienceThis paper investigates the incompressible limit of a system modelling the gro...
International audienceIn this paper, we thoroughly analyze the linearized version of a poromechanics...
We propose a diffuse interface model to describe tumor as a multicomponent deformable porous medium....
International audienceThe mathematical modeling of tumor growth leads to singular " stiff pressure l...
International audienceModels of tissue growth are now well established, in particular in relation to...
In this paper, we consider a multispecies variant of the porous media equation used in cancer modell...
This paper proposes a model for the growth of two interacting populations of cells that do not mix. ...
Both compressible and incompressible porous medium models have been used in the literature to descri...
Both compressible and incompressible porous medium models are used in the literature to describe the...
We study the incompressible limit for a two-species model with applications to tissue growth in the ...
We consider a cross-diffusion model of tumor growth structured by phenotypic trait. We prove the exi...
16 pagesInternational audienceVarious models of tumor growth are available in the litterature. A fir...
We study a two-species model of tissue growth describing dynamics under mechanical pressure and cell...
International audienceModels of tumor growth, now commonly used, present several levels of complexit...
International audienceA mathematical model for tissue growth is considered. This model describes the...
International audienceThis paper investigates the incompressible limit of a system modelling the gro...
International audienceIn this paper, we thoroughly analyze the linearized version of a poromechanics...
We propose a diffuse interface model to describe tumor as a multicomponent deformable porous medium....
International audienceThe mathematical modeling of tumor growth leads to singular " stiff pressure l...
International audienceModels of tissue growth are now well established, in particular in relation to...
In this paper, we consider a multispecies variant of the porous media equation used in cancer modell...
This paper proposes a model for the growth of two interacting populations of cells that do not mix. ...