Zobrazeno 1 - 10
of 43
pro vyhledávání: '"Dębiec, Tomasz"'
In this study, we explore a mathematical model for tissue growth focusing on the interplay between multiple cell subpopulations with distinct phenotypic characteristics. The model addresses the dynamics of tissue growth influenced by phenotype-depend
Externí odkaz:
http://arxiv.org/abs/2409.02904
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 the mechanical pressure and the cell density, the model can be expres
Externí odkaz:
http://arxiv.org/abs/2403.19070
Autor:
Dębiec, Tomasz, Süli, Endre
We consider the Hookean dumbbell model, a system of nonlinear PDEs arising in the kinetic theory of homogeneous dilute polymeric fluids. It consists of the unsteady incompressible Navier-Stokes equations in a bounded Lipschitz domain, coupled to a Fo
Externí odkaz:
http://arxiv.org/abs/2306.16901
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 law, Brinkman's law or Darcy's law. While each of these velocity-pres
Externí odkaz:
http://arxiv.org/abs/2303.10620
We consider several pressureless variants of the compressible Euler equation driven by nonlocal repulsionattraction and alignment forces with Poisson interaction. Under an energy admissibility criterion, we prove existence of global measure-valued so
Externí odkaz:
http://arxiv.org/abs/2109.07536
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 cell-population models to free boundary problems of Hele-Shaw type. A
Externí odkaz:
http://arxiv.org/abs/2108.00787
We prove via convex integration a result that allows to pass from a so-called subsolution of the isentropic Euler equations (in space dimension at least $2$) to exact weak solutions. The method is closely related to the incompressible scheme establis
Externí odkaz:
http://arxiv.org/abs/2107.10618
Autor:
Dębiec, Tomasz, Schmidtchen, Markus
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 context of visco-elastic media, where the velocity field is linke
Externí odkaz:
http://arxiv.org/abs/1910.09498
Autor:
Dębiec, Tomasz
In this work we consider companion conservation laws to general systems of conservation laws. We investigate sufficient regularity for weak solutions to satisfy companion laws, assuming the fluxes to be $C^{1,\gamma}$, $0<\gamma<1$, regular. We discu
Externí odkaz:
http://arxiv.org/abs/1910.05793
Publikováno v:
Analysis & PDE 13 (2020) 789-811
We consider the compressible isentropic Euler equations on $\mathbb{T}^d\times [0,T]$ with a pressure law $p\in C^{1,\gamma-1}$, where $1\le \gamma <2$. This includes all physically relevant cases, e.g.\ the monoatomic gas. We investigate under what
Externí odkaz:
http://arxiv.org/abs/1808.05029