Results 41 to 50 of about 895 (106)

Finite-time blowup in a supercritical quasilinear parabolic-parabolic Keller-Segel system in dimension 2 [PDF]

Acta Applicandae Mathematicae 129, No. 1, 135-146 (2014), 2012
In this paper we prove finite-time blowup of radially symmetric solutions to the quasilinear parabolic-parabolic two-dimensional Keller-Segel system for any positive mass. This is done in case of nonlinear diffusion and also in the case of nonlinear cross-diffusion provided the nonlinear chemosensitivity term is assumed not to decay.
arxiv   +1 more source

A hyperbolic model of chemotaxis on a network: a numerical study [PDF]

ESAIM: M2AN 48 (2014) 231-258, 2012
In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our
arxiv   +1 more source

A Multiscale Model of Biofilm as a Senescence-Structured Fluid

, 2006
We derive a physiologically structured multiscale model for biofilm development. The model has components on two spatial scales, which induce different time scales into the problem.
Bruce P. Ayati, Dockery J., Isaac Klapper   +2 more
core   +2 more sources

A degenerate migration-consumption model in domains of arbitrary dimension

Advanced Nonlinear Studies
In a smoothly bounded convex domain Ω⊂Rn ${\Omega}\subset {\mathbb{R}}^{n}$ with n ≥ 1, a no-flux initial-boundary value problem forut=Δuϕ(v),vt=Δv−uv, $$\begin{cases}_{t}={\Delta}\left(u\phi \left(v\right)\right),\quad \hfill \\ {v}_{t}={\Delta}v-uv ...
Winkler Michael
doaj   +1 more source

The fully parabolic multi-species chemotaxis system in $\mathbb{R}^{2}$

European Journal of Applied Mathematics
This article is devoted to the analysis of the parabolic–parabolic chemotaxis system with multi-components over $\mathbb{R}^2$ . The optimal small initial condition on the global existence of solutions for multi-species chemotaxis model in the ...
Ke Lin
doaj   +1 more source

Travelling wave solutions of the density-suppressed motility model [PDF]

arXiv, 2020
In this paper, we study the traveling wave solutions to the density-suppressed motility model describing the ``self-trapping'' mechanism that induces spatio-temporal pattern formations observed in the experiment. We establish the existence of traveling wavefronts with a minimal wave speed and discuss the selection of wave profiles supplemented with ...
arxiv  

A hybrid mathematical model for self-organizing cell migration in the zebrafish lateral line [PDF]

Journal of Mathematical Biology (2015) 71: 171, 2013
In this paper we propose a "discrete in continuous" mathematical model for the morphogenesis of the posterior lateral line system in zebrafishes. Our model follows closely the results obtained in recent biological experiments. We rely on a hybrid description: discrete for the cellular level and continuous for the molecular level. We prove the existence
arxiv   +1 more source

Generalised supersolutions with mass control for the Keller-Segel system with logarithmic sensitivity

, 2018
The existence of generalised global supersolutions with a control upon the total muss is established for the parabolic-parabolic Keller-Segel system with logarithmic sensitivity for any space dimension.
Zhigun, Anna
core   +1 more source

Proteus mirabilis swarm-colony development with drift [PDF]

arXiv, 2008
We prove a global existence result for a model describing the swarming phenomenon of the bacterium Proteus mirabilis. The model consists of an ordinary differential equation coupled with an age-structured equation involving nonlinear degenerate diffusion and an additional drift term.
arxiv  

Analysis of a model describing bacterial colony expansion in radial geometry driven by chemotaxis

European Journal of Applied Mathematics
We investigate a recent model proposed in the literature elucidating patterns driven by chemotaxis, similar to viscous fingering phenomena. Notably, this model incorporates a singular advection term arising from a modified formulation of Darcy’s law.
Elio Espejo
doaj   +1 more source