Improvement of conditions for asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity [PDF]
arXiv, 2017 This paper deals with the two-species chemotaxis-competition system. About the problem, Bai--Winkler first obtained asymptotic stability under some conditions. Recently, the conditions assumed in the previous work were improved; however, there is a gap between the conditions assumed in the previous works.
arxiv
Low modes regularity criterion for a chemotaxis-Navier-Stokes system [PDF]
arXiv, 2018 In this paper we study the regularity problem of a three dimensional chemotaxis-Navier-Stokes system on a periodic domain. A new regularity criterion in terms of only low modes of the oxygen concentration and the fluid velocity is obtained via a wavenumber splitting approach. The result improves many existing criteria in the literature.
arxiv
A stochastic model for the stepwise motion in actomyosin dynamics
, 2003 A jump-diffusion process is proposed to describe the displacements performed by single myosin heads along actin filaments during the rising phases.
Buonocore, A. +3 more
core
Stochastic differential equation modelling of cancer cell migration and tissue invasion. [PDF]
J Math Biol, 2023 Katsaounis D +2 more
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A Bayesian finite-element trained machine learning approach for predicting post-burn contraction. [PDF]
Neural Comput Appl, 2022 Egberts G +3 more
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Tumor growth towards lower extracellular matrix conductivity regions under Darcy's Law and steady morphology. [PDF]
J Math Biol, 2022 Zheng X, Zhao K, Jackson T, Lowengrub J.
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Sensitivity of a two-dimensional biomorphoelastic model for post-burn contraction. [PDF]
Biomech Model Mechanobiol, 2023 Egberts G +3 more
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Global existence versus blow up for some models of interacting particles [PDF]
Colloq. Math. 106, 2 (2006) 293--303, 2006 We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and the Debye-Hukel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time
arxiv
The parabolic-parabolic Keller-Segel model in $\mathbb{R}^2$ [PDF]
arXiv, 2007 This paper is devoted mainly to the global existence problem for the two-dimensional parabolic-parabolic Keller-Segel in the full space. We derive a critical mass threshold below which global existence is ensured. Using carefully energy methods and ad hoc functional inequalities we improve and extend previous results in this direction.
arxiv
Modelling microtube driven invasion of glioma. [PDF]
J Math Biol, 2023 Hillen T, Loy N, Painter KJ, Thiessen R.
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