1 citations · 1 across the 2 of their papers we have counts for
9 papers
On the Incompressible Limit for a Tumour Growth Model incorporating Convective Effects
Noemi David, Markus Schmidtchen
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 ad…
Many-particle limit for a system of interaction equations driven by Newtonian potentials
Marco Di Francesco, Antonio Esposito, Markus Schmidtchen
We consider a discrete particle system of two species coupled through nonlocal interactions driven by the one-dimensional Newtonian potential, with repulsive self-interaction and a…
The Aronson-Bénilan Estimate in Lebesgue Spaces
Giulia Bevilacqua, Benoît Perthame, Markus Schmidtchen
In a celebrated three-pages long paper in 1979, Aronson and Bénilan obtained a remarkable estimate on second order derivatives for the solution of the porous media equation. Since…
Incompressible limit for a two-species tumour model with coupling through Brinkman's law in one dimension
Tomasz Dębiec, Markus Schmidtchen
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…
Segregation and Gap Formation in Cross-Diffusion Models
M. Burger, J. A. Carrillo, J. -F. Pietschmann +1
In this paper we analyse a class of nonlinear cross-diffusion systems for two species with local repulsive interactions that exhibit a formal gradient flow structure with respect t…
Trend to Equilibrium for Systems with Small Cross-Diffusion
Luca Alasio, Helene Ranetbauer, Markus Schmidtchen +1
This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynam…