Related papers: Chemotaxis on networks: Analysis and numerical app…
To successfully navigate chemical gradients, microorganisms need to predict how the ligand concentration changes in space. Due to their limited size, they do not take a spatial derivative over their body length but rather a temporal…
We investigate a particle system which is a discrete and deterministic approximation of the one-dimensional Keller-Segel equation with a logarithmic potential. The particle system is derived from the gradient flow of the homogeneous free…
In this paper, we study approximation properties of single hidden layer neural networks with weights varying on finitely many directions and thresholds from an open interval. We obtain a necessary and at the same time sufficient measure…
We consider the following chemotaxis model %fully parabolic Keller-Segel system with logistic source $$ \left\{\begin{array}{ll} u_t=\nabla\cdot(D(u)\nabla u)-\chi\nabla\cdot(u\nabla v)+\mu (u-u^2),\quad x\in \Omega, t>0, \disp{v_t-\Delta…
We establish criteria on the chemotactic sensitivity $\chi$ for the non-existence of global weak solutions (i.e. \textit{blow-up} in finite time) to a stochastic Keller--Segel model with spatially inhomogeneous, conservative noise on…
This manuscript deals with the three-dimensional version of a flux-limited Keller-Segel system coupled to the incompressible Stokes equations through transport and buoyancy. The main goal consists in verifying that within a certain…
We seek the best traffic allocation scheme for the edge-cloud computing network that satisfies constraints and minimizes the cost based on burstable billing. First, for a fixed network topology, we formulate a family of integer programming…
We construct weak global in time solutions to the classical Keller-Segel system cell movement by chemotaxis in two dimensions when the total mass is below the well-known critical value. Our construction takes advantage of the fact that the…
In this work, we develop a novel numerical scheme to solve the classical Keller--Segel (KS) model which simultaneously preserves its intrinsic mathematical structure and achieves optimal accuracy. The model is reformulated into a gradient…
This article deals with the logistic Keller-Segel model \[ \begin{cases} u_t = \Delta u - \chi \nabla\cdot(u\nabla v) + \kappa u - \mu u^2, \\ \\ v_t = \Delta v - v + u \end{cases} \] in bounded two-dimensional domains (with homogeneous…
We study a system of two coupled nonlinear parabolic equations. It constitutes a variant of the Keller-Segel model for chemotaxis, i.e. it models the behaviour of a population of bacteria that interact by means of a signalling substance. We…
Two relaxation features of the migration-consumption chemotaxis system involving signal-dependent motilities, $$ \left\{ \begin{array}{l} u_t = \Delta \big(u\phi(v)\big), \\[1mm] v_t = \Delta v-uv, \end{array} \right. \qquad \qquad…
In this paper, we study the classical Keller - Segel system on a two-dimensional domain perturbed by a pair of Wiener processes, where the leading diffusion term is replaced by a porous media term. Since the randomness is intrinsic, the…
This paper studies the non-negative solutions of the Keller-Segel model with a nonlocal nonlinear source in a bounded domain. The competition between the aggregation and the nonlocal reaction term is highlighted: when the growth factor is…
This paper deals with a sub-critical Keller-Segel equation. Starting from the stochastic particle system associated with it, we show well-posedness results and the propagation of chaos property. More precisely, we show that the empirical…
In this paper we develop a numerical scheme for approximating a $d$-dimensional chemotaxis-Navier-Stokes system, $d=2,3$, modeling cellular swimming in incompressible fluids. This model describes the chemotaxis-fluid interaction in cases…
Chemotaxis plays a crucial role in a variety of processes in biology and ecology. Quite often it acts to improve efficiency of biological reactions; one example is the immune system signalling, where infected tissues release chemokines…
Unboundedness of solutions is shown to occur in a one-dimensional quasilinear parabolicparabolic chemotaxis system for any initial mass. Our result is also independent of the relation between the speeds of the diffusion of cells and…
We consider a stochastic Keller-Segel-Navier-Stokes system in $R^2$ describing the collective motion of cells in an ambient stochastic fluid flow, where the cells are attracted by a chemical substance and transported by the ambient fluid…
We consider a parabolic-elliptic Keller-Segel type system, which is related to a simplified model of chemotaxis. Concerning the maximal range of existence of solutions, there are essentially two kinds of results: either global existence in…