相关论文: Remarks on two connected papers about Keller-Segel…
This paper studies the quantitative unique continuation for a semi-linear parabolic-elliptic coupled system on a bounded domain. This system is a simplified version of the chemotaxis model introduced by Keller and Segel. With the aid of…
This paper establishes the global uniform-in-time boundedness of solutions to the following Keller-Setel system with signal-dependent diffusion and chemotaxis \begin{equation}\left\{ \begin{array}{ll} u_t=\nabla\cdot(\gamma(v)\nabla u -…
We consider the quasilinear parabolic-parabolic Keller-Segel system $$ u_t=\nabla \cdot (D(u)\nabla u) - \nabla \cdot (S(u)\nabla v), \qquad x\in\Omega, \ t>0, v_t=\Delta v -v + u, x\in\Omega, \ t>0, $$ under homogeneous Neumann boundary…
We introduce stochastic models of chemotaxis generalizing the deterministic Keller-Segel model. These models include fluctuations which are important in systems with small particle numbers or close to a critical point. Following Dean's…
This paper deals with convergence of a solution for the parabolic-parabolic Keller-Segel system \[ (u_\lambda)_t = \Delta u_\lambda - \chi \nabla \cdot (u_\lambda \nabla v_\lambda), \quad \lambda (v_\lambda)_t = \Delta v_\lambda - v_\lambda…
We consider the Keller-Segel system with logical source \begin{align*} \begin{cases} u_t = \nabla \cdot (\phi(u)\nabla u) - \nabla \cdot (\psi(u)\nabla v)+f(u), & x \in \Omega, \; t > 0, v_t = \Delta v - v + u, & x \in \Omega, \; t > 0,…
This paper deals with the Keller--Segel system with signal-dependent sensitivity \begin{equation*} u_t=\Delta u - \nabla \cdot (u \chi(v)\nabla v), \quad v_t=\Delta v + u - v, \quad x\in\Omega,\ t>0, \end{equation*} where $\Omega$ is a…
In this paper, we study the following parabolic chemo-repulsion with nonlinear production model: $$ \left\{ \begin{array}{rcl} \partial_tu-\Delta u&=&\nabla\cdot(u\nabla v),\\ \partial_tv-\Delta v+v&=&u^p+fv\, 1_{\Omega_c}. \end{array}…
It is known that, for the parabolic-elliptic Keller-Segel system with critical porous-medium diffusion in dimension $\RR^d$, $d \ge 3$ (also referred to as the quasilinear Smoluchowski-Poisson equation), there is a critical value of the…
We study the following Keller-Segel chemotaxis system with logistic source and nonlinear secretion: \begin{align*} u_t=\Delta u- \nabla\cdot(u\nabla v)+\kappa(|x|)u-\mu(|x|)u^p\quad\text{and}\quad 0=\Delta v-v+u^\gamma, \end{align*} where…
We study some zero-flux attraction-repulsion chemotaxis models, with nonlinear production rates for the chemorepellent and the chemoattractant. This paper partially improves some known results in the literature and moreover solves an open…
A semilinear version of parabolic-elliptic Keller-Segel system with the \emph{critical} nonlocal diffusion is considered in one space dimension. We show boundedness of weak solutions under very general conditions on our semilinearity. It…
We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable…
This paper deals with convergence of solutions to a class of parabolic Keller-Segel systems, possibly coupled to the (Navier-)Stokes equations in the framework of the full model \begin{eqnarray*} \left\{ \begin{array}{lcl} \, \, \partial_t…
The aim of this paper is to provide the analysis result for the partial differential equations arising from the rigorous derivation of the degenerate parabolic-elliptic Keller-Segel system from a moderately interacting stochastic particle…
The purpose of the paper is twofold. Firstly, we want to present a Meta Theorem to show the existence of a martingale solution for coupled systems of non-linear stochastic differential equations. The idea is first to split the system by…
This paper investigates an initial-Neumann boundary value problem for a Keller--Segel system with parabolic-parabolic-ODE coupling. The model incorporates a signal-dependent, non-increasing motility function that, through indirect signal…
We study the global existence of the parabolic-parabolic Keller-Segel system in $\R^d , d \ge 2$. We prove that initial data of arbitrary size give rise to global solutions provided the diffusion parameter $\tau$ is large enough in the…
We study a semilinear and nonlocal Neumann problem, which is the fractional analogue of the problem considered by Lin--Ni--Takagi in the '80s. The model under consideration arises in the description of stationary configurations of the…
This work deals with a fully parabolic chemotaxis model with nonlinear production and chemoattractant. The problem is formulated on a bounded domain and, depending on a specific interplay between the coefficients associated to such…