On the incompressible limit for a tumour growth model incorporating convective effects
N David, M Schmidtchen - Communications on Pure and …, 2024 - Wiley Online Library
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 …
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 …
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 …
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 …
Phenotypic heterogeneity in a model of tumour growth: existence of solutions and incompressible limit
N David - Communications in Partial Differential Equations, 2023 - Taylor & Francis
We consider a (degenerate) cross-diffusion model of tumour growth structured by
phenotypic trait. We prove the existence of weak solutions and the incompressible limit as …
phenotypic trait. We prove the existence of weak solutions and the incompressible limit as …
Nonlocal Cahn–Hilliard Equation with Degenerate Mobility: Incompressible Limit and Convergence to Stationary States
The link between compressible models of tissue growth and the Hele–Shaw free boundary
problem of fluid mechanics has recently attracted a lot of attention. In most of these models …
problem of fluid mechanics has recently attracted a lot of attention. In most of these models …
Incompressible limit of porous media equation with chemotaxis and growth
Q He, HL Li, B Perthame - arXiv preprint arXiv:2312.16869, 2023 - arxiv.org
We revisit the problem of proving the incompressible limit for the compressible porous media
equation with Newtonian drift and growth. The question is motivated by models of living …
equation with Newtonian drift and growth. The question is motivated by models of living …
On the inviscid limit connecting Brinkman's and Darcy's models of tissue growth with nonlinear pressure
C Elbar, J Skrzeczkowski - arXiv preprint arXiv:2306.03752, 2023 - arxiv.org
Several recent papers have addressed modelling of the tissue growth by the multi-phase
models where the velocity is related to the pressure by one of the physical laws (Stoke's …
models where the velocity is related to the pressure by one of the physical laws (Stoke's …
Existence of solutions to reaction cross diffusion systems
M Jacobs - SIAM Journal on Mathematical Analysis, 2023 - SIAM
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 …
equation. These systems play an important role in the mechanical modeling of living tissues …
Pressure jump and radial stationary solutions of the degenerate Cahn-Hilliard equation
C Elbar, B Perthame, J Skrzeczkowski - arXiv preprint arXiv:2206.07451, 2022 - arxiv.org
The Cahn-Hilliard equation with degenerate mobility is used in several areas including the
modeling of living tissues. We are interested in quantifying the pressure jump at the interface …
modeling of living tissues. We are interested in quantifying the pressure jump at the interface …