Results 21 to 30 of about 895 (106)
Stability Analysis of a Model of Atherogenesis: An Energy Estimate Approach
Computational and Mathematical Methods in Medicine, Volume 9, Issue 2, Page 121-142, 2008., 2008 Atherosclerosis is a disease of the vasculature that is characterized by chronic inflammation and the accumulation of lipids and apoptotic cells in the walls of large arteries. This disease results in plaque growth in an infected artery typically leading to occlusion of the artery. Atherosclerosis is the leading cause of human mortality in the US, much
A. I. Ibragimov +3 more
wiley +1 more source
Mathematical models of cell self-organization
Journal of the Egyptian Mathematical Society, 2011 Various classes of Partial Differential Equations have shown to be successful in describing the self-organization of bacterial colonies, a topic also sometimes called socio-biology. For instance parabolic systems are standard; the classical Patlak–Keller–
Benoît Perthame
doaj +1 more source
Advances in Nonlinear Analysis, 2019 In bounded n-dimensional domains Ω, the Neumann problem for the parabolic ...
Winkler Michael
doaj +1 more source
Modelling cell movement and chemotaxis pseudopod based feedback [PDF]
, 2011 A computational framework is presented for the simulation of eukaryotic cell migration and chemotaxis. An empirical pattern formation model, based on a system of non-linear reaction-diffusion equations, is approximated on an evolving cell boundary using ...
Insall, Robert H. +3 more
core +1 more source
A multiscale model of cell mobility: From a kinetic to a hydrodynamic description [PDF]
, 2014 This paper concerns a model for tumor cell migration through the surrounding extracellular matrix by considering mass balance phenomena involving the chemical interactions produced on the cell surface. The well-posedness of this model is proven. An asymptotic analysis via a suitable hydrodynamic limit completes the description of the macroscopic ...
arxiv +1 more source
bioRxivCell sorting by differential adhesion is one of the basic mechanisms explaining spatial organization of neurons in early stage brain development of fruit flies.
José A. Carrillo +3 more
semanticscholar +1 more source
Global existence for a degenerate haptotaxis model of cancer invasion [PDF]
, 2015 We propose and study a strongly coupled PDE-ODE system with tissue-dependent degenerate diffusion and haptotaxis that can serve as a model prototype for cancer cell invasion through the extracellular matrix. We prove the global existence of weak solutions and illustrate the model behaviour by numerical simulations for a two-dimensional setting.
arxiv +1 more source
A kinetic chemotaxis model with internal states and temporal sensing [PDF]
arXiv, 2021 By employing the Fourier transform to derive key a priori estimates for the temporal gradient of the chemical signal, we establish the existence of global solutions and hydrodynamic limit of a chemotactic kinetic model with internal states and temporal gradient in one dimension, which is a system of two transport equations coupled to a parabolic ...
arxiv
Hölder estimates of weak solutions to degenerate chemotaxis systems with a source term [PDF]
arXiv, 2022 In this note we consider degenerate chemotaxis systems with porous media type diffusion and a source term satisfying the Hadamard growth condition. We prove the H\"older regularity for bounded solutions to parabolic-parabolic as well as for elliptic-parabolic chemotaxis systems.
arxiv
Global Existence and Asymptotic Behavior of Solutions to a Chemotaxis-Fluid System on General Bounded Domain [PDF]
, 2014 In this paper, we investigate an initial-boundary value problem for a chemotaxis-fluid system in a general bounded regular domain $\Omega \subset \mathbb{R}^N$ ($N\in\{2,3\}$), not necessarily being convex.
Jiang, Jie, Wu, Hao, Zheng, Songmu
core