Free boundary limit of a tumor growth model with nutrient
N David, B Perthame - Journal de Mathématiques Pures et Appliquées, 2021 - Elsevier
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 …
describe the mechanical properties of living tissues. These two classes of models can be …
On the incompressible limit for a tumour growth model incorporating convective effects
In this work we study a tissue growth model with applications to tumour growth. The model is
based on that of Perthame, Quirós, and Vázquez proposed in 2014 but incorporates the …
based on that of Perthame, Quirós, and Vázquez proposed in 2014 but incorporates the …
[HTML][HTML] Incompressible limit for a two-species model with coupling through Brinkman's law in any dimension
T Dębiec, B Perthame, M Schmidtchen… - … de Mathématiques Pures …, 2021 - Elsevier
We study the incompressible limit for a two-species model with applications to tissue growth
in the case of coupling through the so-called Brinkman's law in any space dimensions. The …
in the case of coupling through the so-called Brinkman's law in any space dimensions. The …
Incompressible limits of the Patlak-Keller-Segel model and its stationary state
Q He, HL Li, B Perthame - Acta Applicandae Mathematicae, 2023 - Springer
We complete previous results about the incompressible limit of both the n-dimensional (n≥
3) compressible Patlak-Keller-Segel (PKS) model and its stationary state. As in previous …
3) compressible Patlak-Keller-Segel (PKS) model and its stationary state. As in previous …
Hele–shaw limit for a system of two reaction-(cross-) diffusion equations for living tissues
Multiphase mechanical models are now commonly used to describe living tissues including
tumour growth. The specific model we study here consists of two equations of mixed …
tumour growth. The specific model we study here consists of two equations of mixed …
Convergence rate for the incompressible limit of nonlinear diffusion–advection equations
N David, T Dębiec, B Perthame - Annales de l'Institut Henri Poincaré C, 2022 - ems.press
The incompressible limit of nonlinear diffusion equations of porous medium type has
attracted a lot of attention in recent years, due to its ability to link the weak formulation of …
attracted a lot of attention in recent years, due to its ability to link the weak formulation of …
Incompressible limit for a two-species tumour model with coupling through Brinkman's law in one dimension
T Dębiec, M Schmidtchen - Acta Applicandae Mathematicae, 2020 - Springer
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 coupling of both species through the so-called Brinkman law which is typically used in …
A degenerate cross-diffusion system as the inviscid limit of a nonlocal tissue growth model
In recent years, there has been a spike in interest in multiphase tissue growth models.
Depending on the type of tissue, the velocity is linked to the pressure through Stoke's law …
Depending on the type of tissue, the velocity is linked to the pressure through Stoke's law …
Global existence theorem for a model governing the motion of two cell populations
This article is concerned with the existence of a weak solution to the initial boundary
problem for a cross-diffusion system which arises in the study of two cell population growth …
problem for a cross-diffusion system which arises in the study of two cell population growth …
Incompressible limit of a continuum model of tissue growth for two cell populations
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 …
cells population. The model describes the dynamics of cell densities, driven by pressure …