4 papers
Incompressible limit for a two-species Brinkman model with drift
Tomasz Dębiec, Valentin Vincent Neumann, Markus Schmidtchen
We study a two-species model for tissue growth in which both populations are transported by an external drift and by a velocity potential determined through Brinkman's law. The pre…
Stability of solutions of the porous medium equation with growth with respect to the diffusion exponent
Tomasz Dębiec, Piotr Gwiazda, Błażej Miasojedow +1
We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between…
A Degenerate Cross-Diffusion System as the Inviscid Limit of a Nonlocal Tissue Growth Model
Noemi David, Tomasz Dębiec, Mainak Mandal +1
In recent years, there has been a spike in the interest in multi-phase tissue growth models. Depending on the type of tissue, the velocity is linked to the pressure through Stoke's…
Dissipative measure-valued solutions to the Euler-Poisson equation
José A. Carrillo, Tomasz Dębiec, Piotr Gwiazda +1
We consider several pressureless variants of the compressible Euler equation driven by nonlocal repulsionattraction and alignment forces with Poisson interaction. Under an energy a…