Related papers: Mathematical treatment of PDE model describing che…
We study a modified version of an initial-boundary value problem describing the formation of colony patterns of bacteria \textit{Escherichia Coli}. The original system of three parabolic equations was studied numerically and analytically…
A Keller-Segel model describes macroscopic dynamics of bacterial colonies and biological cells. Bacteria secret chemical which attracts other bacteria so that they move towards chemical gradient creating nonlocal attraction between…
We study a new nonlocal approach to the mathematical modelling of the Chemotaxis problem, which describes the random motion of a certain population due a substance concentration. Considering the initial-boundary value problem for the…
In this paper, we study the initial-boundary value problem and its asymptotic behavior for a repulsive chemotaxis model with logarithmic sensitivity and logistic growth. We establish global well-posedness of strong solutions for large…
Motile bacteria can migrate along chemical gradients in a process known as chemotaxis. When exposed to uniform environmental stress, Escherichia coli cells coordinate their chemotactic responses to form millimeter-sized condensates…
An analysis of traveling wave solutions of partial differential equation (PDE) systems with cross-diffusion is presented. The systems under study fall in a general class of the classical Keller-Segel models to describe chemotaxis. The…
Chemotaxis in bacteria such as \textit{E.\ coli} is controlled by the slow methylation of chemoreceptors. As a consequence, intrinsic time and length scales of tens of seconds and hundreds of micrometers emerge, making the Keller--Segel…
We study the stationary Keller--Segel chemotaxis models with logistic cellular growth over a one-dimensional region subject to the Neumann boundary condition. We show that nonconstant solutions emerge in the sense of Turing's instability as…
We consider a Liouville-type PDE on a smooth bounded planar domain, which is related to stationary solutions of the Keller-Segel's model for chemotaxis. We prove existence of solutions under some algebraic conditions on the parameters. In…
We consider the boundary value problem $-\Delta u + u =\lambda e^u$ in $\Omega$ with Neumann boundary condition, where $\Omega$ is a bounded smooth domain in $\mathbb R^2$, $\lambda>0.$ This problem is equivalent to the stationary…
It is of great biological interest to understand the molecular origins of chemotactic behavior of E. coli by developing population-level models based on the underlying signaling pathway dynamics. We derive macroscopic models for E.coli…
We consider the singular limit of a chemotaxis model of bacterial collective motion recently introduced in arXiv:2009.11048 [math.AP]. The equation models aggregation-diffusion phenomena with advection that is discontinuous and depends…
The celebrated experiment of Tuval et al. \cite{tuval2005bacterial} showed that the bacteria living a water drop can form a thin layer near the air-water interface, where a so-called chemotaxis-fluid system with physical boundary conditions…
A pathway-based mean-field theory (PBMFT) was recently proposed for E. coli chemotaxis in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys. Rev. Lett., 109 (2012), 048101]. In this paper, we derived a new moment system of PBMFT by using the moment…
The existence and nonexistence of global in time solutions is studied for a class of equations generalizing the chemotaxis model of Keller and Segel. These equations involve L\'evy diffusion operators and general potential type nonlinear…
This study investigates an SEIS PDE model with a free boundary, which captures the dynamics of epidemic transmission, including diseases like COVID-19. This parabolic PDE system is analyzed in a rotationally symmetric domain, and the…
This paper is devoted to constructing approximate solutions for the classical Keller--Segel model governing \emph{chemotaxis}. It consists of a system of nonlinear parabolic equations, where the unknowns are the average density of cells (or…
Various bacterial strains exhibit colonial branching patterns during growth on poor substrates. These patterns reflect bacterial cooperative self-organization and cybernetic processes of communication, regulation and control employed during…
This paper is concerned with the asymptotic stability of the initial-boundary value problem of a singular PDE-ODE hybrid chemotaxis system in the half space $\R_+=[0, \infty)$. We show that when the non-zero flux boundary condition at $x=0$…
The Keller-Segel model is a system of partial differential equations modelling chemotactic aggregation in cellular systems. This model has blowing up solutions for large enough initial conditions in dimensions d >= 2, but all the solutions…