Related papers: Blow-up, concentration phenomenon and global exist…
In this paper, we obtain upper bounds for the critical time $T^*$ of the blow-up for the parabolic-elliptic Patlak-Keller-Segel system on the 2D-Euclidean space. No moment condition or/and entropy condition are required on the initial data;…
The aim of this paper is to analyze a model for chemotaxis based on a local sensing mechanism instead of the gradient sensing mechanism used in the celebrated minimal Keller-Segel model. The model we study has the same entropy as the…
In this paper, we consider a Keller-Segel model with a fractional diffusion term in $\mathbb{R}^3$ in the background of a Couette flow. We show that when the background Couette flow is large enough, the dissipation enhancement induced could…
In this paper, we consider the Cauchy problem for a generalized parabolic-elliptic Keller-Segel equation with fractional dissipation and the additional mixing effect of advection by an incompressible flow. Under suitable mixing condition on…
In this paper, we consider the Cauchy problem for the three dimensional parabolic-elliptic Keller-Segel equation with a large non-shear incompressible flow. Without advection, there exist solution with arbitrarily mass which blow up in…
In this paper we prove that the full Keller-Segel system, a quasilinear strongly coupled reaction-crossdiffusion system of four parabolic equations, is well-posed in space dimensions 2 and 3 in the sense that it always admits an unique…
Consider a class of chemotaxis-fluid model incorporating a volume-filling effect in the sense of Painter and Hillen (Can. Appl. Math. Q. 2002; 10(4): 501-543), which is a supercritical parabolic-elliptic Keller-Segel system. As shown by…
This paper deals with the quasilinear parabolic-elliptic Keller-Segel system with logistic source, \begin{align*} u_t=\Delta (u+1)^m - \chi \nabla \cdot (u(u+1)^{\alpha - 1} \nabla v) + \lambda(|x|) u - \mu(|x|) u^\kappa, \quad 0=\Delta v -…
We consider a model of cell motion with boundary signal production which describes some aspects of eukaryotic cell migration. Generic polarity markers located in the cell are transported by actin which they help to polymerize. This leads to…
Based on the method of matched asymptotic expansions and Banach fixed point theorem, we rigorously construct infinitely many self-similar blow-up profiles for the parabolic-elliptic Keller-Segel system \begin{equation*}…
We study the solutions of the two-dimensional Keller-Segel system describing chemotaxis. The Keller-Segel system as well as the properties of the blow-up set has been extensively studied. In this paper we obtain generalized solutions for…
This work is a series of two articles. The main goal is to rigorously derive the degenerate parabolic-elliptic Keller-Segel system in the sub-critical regime from a moderately interacting stochastic particle system. In the first article…
We study radial solutions in a ball of $\mathbb{R}^N$ of a semilinear, parabolic-elliptic Patlak-Keller-Segel system with a nonlinear sensitivity involving a critical power. For $N = 2$, the latter reduces to the classical linear model,…
We analyze blowup solutions in infinite time of the Neumann boundary value problem for the fully parabolic chemotaxis system with local sensing: \begin{equation*} \begin{cases} u_t = \Delta(e^{-v}u)\qquad &\mathrm{in}\ \Omega \times…
We construct axially symmetric finite-time blow-up solutions to the three-dimensional Keller-Segel system. By adapting gluing techniques, we derive a precise asymptotic expansion for Type II singularities that generalizes the recent work of…
In this paper we consider a stochastic Keller-Segel type equation, perturbed with random noise. We establish that for special types of random pertubations (i.e. in a divergence form), the equation has a global weak solution for small…
In this paper we deal with diffusive relaxation limits of nonlinear systems of Euler type modeling chemotactic movement of cells toward Keller--Segel type systems. The approximating systems are either hyperbolic--parabolic or…
In this work, we investigate the dynamics of a non-local model describing spontaneous cell polarisation. It consists in a drift-diffusion equation set in the half-space, with the coupling involving the trace value on the boundary. We…
\indent In this paper, we study a class of parabolic-elliptic Keller-Segel systems with diffusion sensitivity dependent on spatial position, given by type \begin{equation} \left\{ \begin{array}{ll} u_{t} = \bigtriangledown\cdot(|x|^{\beta}…
In this paper, we investigate to the existence and uniqueness of periodic solutions for the parabolic-elliptic Keller-Segel system on whole spaces detailized by Euclidean space $\mathbb{R}^n\,\,(\hbox{ where }n \geqslant 4)$ and real…