Related papers: Uniqueness for Keller-Segel-type chemotaxis models
In this paper, we propose a numerical scheme to solve the kinetic model for chemotaxis phenomena. Formally, this scheme is shown to be uniformly stable with respect to the small parameter, consistent with the fluid-diffusion limit…
In this paper, the well-posedness of two-dimensional signal-dependent Keller-Segel system and its mean-field derivation from a interacting particle system on the whole space are investigated. The signal dependence effect is reflected by the…
We introduce a novel gradient-based damping term into a Keller-Segel type taxis model with motivation from ecology and consider the following system equipped with homogeneous Neumann-boundary conditions: \begin{equation} \begin{cases} u_t=…
We consider a one-dimensional system arising from a chemotaxis model in tumour angiogenesis, which is described by a Keller-Segel equation with singular sensitivity. This hyperbolic-parabolic system is known to allow viscous shocks…
This paper is devoted to the analysis of the classical Keller-Segel system over $\mathbb{R}^d$, $d\geq 3$. We describe as much as possible the dynamics of the system characterized by various criteria, both in the parabolic-elliptic case and…
We consider aggregation-diffusion equations with merely bounded nonlocal interaction potential $K$. We are interested in establishing their well-posedness theory when the nonlocal interaction potential $K$ is neither differentiable nor…
We study the chemotaxis-fluid system \begin{align*} \left\{\begin{array}{r@{\,}l@{\quad}l@{\,}c} n_{t}&=\Delta n-\nabla\!\cdot(n\nabla c)-u\cdot\!\nabla n,\ &x\in\Omega,& t>0,\\ c_{t}&=\Delta c-c+f(n)-u\cdot\!\nabla c,\ &x\in\Omega,& t>0,\\…
We investigate the large-time behavior of the solutions of the two-dimensional Keller-Segel system in self-similar variables, when the total mass is subcritical, that is less than 8\pi after a proper adimensionalization. It was known from…
We study the properties of a semi-implicit Euler scheme that is widely used in time discretization of Keller-Segel equations both in the parabolic-elliptic form and the parabolic-parabolic form. We prove that this linear, decoupled,…
This paper investigates a two-dimensional Keller--Segel--Navier--Stokes system with a tensor-valued chemotactic sensitivity $S(x,n,c)$. Under a signal-dependent power-decay condition $|S(x,n,c)| \le s_0 (s_1+c)^{-\gamma}$, we establish the…
In this paper, the fully parabolic Keller-Segel system \begin{equation} \left\{ \begin{array}{llc} u_t=\Delta u-\nabla\cdot(u\nabla v), &(x,t)\in \Omega\times (0,T),\\ v_t=\Delta v-v+u, &(x,t)\in\Omega\times (0,T),\\ \end{array} \right.…
As it is well known, the parabolic-elliptic Keller-Segel system of chemotaxis on the plane has global-in-time regular nonnegative solutions with total mass below the critical value $8\pi$. Solutions with mass above $8\pi$ blow up in a…
Consider the coupled Keller-Segel-Navier-Stokes or the chemotaxis-consumption-Navier-Stokes system in bounded Lipschitz domains for general coupling terms which, e.g., include buoyancy forces. It is shown that these systems admit local…
Auto-chemotaxis, the directed movement of cells along gradients in chemicals they secrete, is central to the formation of complex spatiotemporal patterns in biological systems. Since the introduction of the Keller--Segel model, numerous…
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…
We study the following Neumann boundary problem related to the stationary solutions of the Keller-Segel system, a basic model of chemotaxis phenomena: \[ \left\{\begin{array}{ll} -\Delta_g u +\beta u =\lambda\left(\frac{Ve^u}{\int_{\Sigma}…
The current paper is concerned with the forced waves of Keller-Segel chemoattraction systems in shifting environments of the form, \begin{equation} \begin{cases} u_t=u_{xx}-\chi(uv_x)_x +u(r(x-ct)-bu),\quad x\in\mathbb{R}\cr 0=v_{xx}- \nu…
We consider the parabolic-elliptic Keller-Segel system in three dimensions and higher, corresponding to the mass supercritical case. We construct rigorously a solution which blows up in finite time by having its mass concentrating near a…
For a Keller-Segel model for chemotaxis in two spatial dimensions we consider a modification of a positivity preserving fully discrete scheme using a local extremum diminishing flux limiter. We discretize space using piecewise linear finite…
Aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with nonlinear diffusion are popular models for nonlocal aggregation phenomenon and are a source of a number of interesting mathematical problems in nonlinear PDE.…