On existence of solutions for some hyperbolic-parabolic-type chemotaxis systems

In this paper, we discuss the local and global existence ofweak solutions for some hyperbolic–parabolic systems modellingchemotaxis.     

Global existence and time decay estimate of solutions to the Keller–Segel system

We consider the chemotaxis‐Navier–Stokes system 1.1-1.4 (Keller–Segel system) in the whole space, which describes the motion of oxygen‐driven bacteria, eukaryotes, in a fluid. We proved the global existence and time decay estimate of solutions to the Cauchy problem 1.1-1.2 in with the small initial data. Moreover, when the fluid motion is described by the Stokes equations, we established the global weak solutions to 1.3-1.4 in with the potential function ? is small and the initial density n₀(x) has finite mass.     

Cooperative Chemotaxis of Magnesium Microswimmers for Corrosion Spotting

Numerous artificial micro- and nanomotors, as well as various swimmers have been inspired by living organisms that are able to move in a coordinated manner. Their cooperation has also gained a lot of attention because the resulting clusters are able to adapt to changes in their environment and to perform complex tasks. However, mimicking such a collective behavior remains a challenge. In the present work, magnesium microparticles are used as chemotactic swimmers with pronounced collective features, allowing the gradual formation of macroscopic agglomerates. The formed clusters act like a single swimmer able to follow pH gradients. This dynamic behavior can be used to spot localized corrosion events in a straightforward way. The autonomous docking of the swimmers to the corrosion site leads to the formation of a local protection layer, thus increasing corrosion resistance and triggering partial self-healing.     

Chemo‐ and Magnetotaxis of Self‐Propelled Light‐Emitting Chemo‐electronic Swimmers

Miniaturized autonomous chemo‐electronic swimmers, based on the coupling of spontaneous oxidation and reduction reactions at the two poles of light‐emitting diodes (LEDs), are presented as chemotactic and magnetotactic devices. In homogeneous aqueous media, random motion caused by a bubble‐induced propulsion mechanism is observed. However, in an inhomogeneous environment, the self‐propelled devices exhibit positive chemotactic behavior, propelling themselves along a pH or ionic strength gradient (?pH and ?I, respectively) in order to reach a thermodynamically higher active state. In addition, the intrinsic permanent magnetic moment of the LED allows self‐orientation in the terrestrial magnetic field or following other external magnetic perturbations, which enables a directional motion control coupled with light emission. The interplay between chemotaxis and magnetotaxis allows fine‐tuning of the dynamic behavior of these swimmers.     

一类带反应项的多种群趋化性模型解的性态(英文)

本文研究了一类带反应的多种群趋化性Othmer-Stevens模型的问题,利用抛物方程上下解和迭代的方法,获得了该模型在不同条件下的解的爆破,熄灭等渐进性态,推广了单种群模型的结果。     

Shock formation in a chemotaxis model

In this paper, we establish the existence of shock solutions for a simplified version of the Othmer–Stevens chemotaxis model (SIAM J. Appl. Math. 1997; 57 :1044–1081). The existence of these shock solutions was suggested by Levine and Sleeman (SIAM J. Appl. Math. 1997; 57 :683–730). Here, we consider the general Riemann problem and derive the shock curves in parameterized forms. By studying the travelling wave solutions, we examine the shock structure for the chemotaxis model and prove that the travelling wave speed is identical to the shock speed. Moreover, we explicitly derive an entropy–entropy flux pair to prove the uniqueness of the weak shock solutions. Some discussion is given for further study. Copyright © 2007 John Wiley & Sons, Ltd.     

一类非线性chemotaxis系统的局部零能控性

本文研究了一类非线性chemotaxis系统的能控性问题.利用这类线性化结合不动点的方法,获得了非线性系统的局部零能控性结果,推广了非线性抛物-椭圆型方程能控性的结果.     

Asymptotic nonlinear stability of a composite wave of two traveling waves to a chemotaxis model

In this paper, we investigate the asymptotic stability of a composite wave consisting of two traveling waves to a Keller–Segel chemotaxis model with logarithmic sensitivity and nonzero chemical diffusion. We show that the composite wave is asymptotically stable under general initial perturbation, which only be needed small in H¹‐norm. This improves previous results. Copyright © 2017 John Wiley & Sons, Ltd.     

Global boundedness in a quasilinear chemotaxis model with nonlinear diffusion and consumption of chemoattractant

This paper proves the global existence and boundedness of solutions to a quasilinear chemotaxis model with nonlinear diffusion and consumption of chemoattractant defined on a smooth bounded domain with no‐flux boundary conditions under some assumptions. The result holds for arbitrary nonnegative sensitivity coefficients and domains in the spatial dimension which is no less than two.