相关论文: Keller-Segel model with Logarithmic Interaction an…
A degenerate Keller-Segel system with diffusion exponent $2n/(n+2)<m<2-\frac{2}{n}$ in multi dimension is studied. An exact criterion for global existence and blow up of solution is obtained. The estimates on $L^{2n/(n+2)}$ norm of the…
We investigate blow-up properties for the initial-boundary value problem of a Keller-Segel model with consumption of chemoattractant when the spatial dimension is three. Through a kinetic reformulation of the Keller-Segel model, we first…
We study the finite-time blow-up in two variants of the parabolic-elliptic Keller-Segel system with nonlinear diffusion and logistic source. In $n$-dimensional balls, we consider \begin{align*} \begin{cases} u_t = \nabla \cdot…
It is known that solutions of the parabolic elliptic Keller-Segel equations in the two dimensional plane decay, as time goes to infinity, provided the initial data admits sub-critical mass and finite second moments, while such solution…
This paper is concerned with the parabolic-elliptic Keller-Segel system with nonlinear diffusion and signal-dependent sensitivity \begin{align}\tag{KS}\label{system} \begin{cases} u_t=\Delta(u+1)^m-\nabla\cdot(u\chi(v)\nabla v),\quad…
We consider two-dimensional versions of the Keller--Segel model for the chemotaxis with either classical (Brownian) or fractional (anomalous) diffusion. Criteria for blowup of solutions in terms of suitable Morrey spaces norms are derived.…
This paper deals with a hyperbolic Keller-Segel system of consumption type with the logarithmic sensitivity \begin{equation*} \partial_{t} \rho = - \chi\nabla \cdot \left (\rho \nabla \log c\right),\quad \partial_{t} c = - \mu c\rho\quad…
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…
We study the blow-up asymptotics of radially decreasing solutions of the parabolic-elliptic Keller-Segel-Patlak system in space dimensions $n\ge 3$. In view of the biological background of this system and of its mass conservation property,…
\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}…
We examine the possibility of finite-time blow-up of solutions to the fully parabolic quasilinear Keller--Segel model \begin{align}\tag{$\star$}\label{prob:star} \begin{cases} u_t = \nabla \cdot ((u+1)^{m-1}\nabla u - u(u+1)^{q-1}\nabla v)…
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.…
The Keller-Segel-Navier-Stokes system governs chemotaxis in liquid environments. This system is to be solved for the organism and chemoattractant densities and for the fluid velocity and pressure. It is known that if the total initial cell…
We construct axisymmetric solutions to the three-dimensional parabolic-elliptic Keller-Segel system that blows up in finite time. In particular, the singularity is of type II, which admits locally a leading order profile of the rescaled…
We consider a Keller-Segel model with non-linear porous medium type diffusion and nonlocal attractive power law interaction, focusing on potentials that are less singular than Newtonian interaction. Here, the nonlinear diffusion is chosen…
In this paper we prove finite-time blowup of radially symmetric solutions to the quasilinear parabolic-parabolic two-dimensional Keller-Segel system for any positive mass. This is done in case of nonlinear diffusion and also in the case of…
It is well-known that the two-dimensional Keller-Segel system admits finite time blowup solutions, which is the case if the initial density has a total mass greater than $8\pi$ and a finite second moment. Several constructive examples of…
This paper deals with the fully parabolic chemotaxis system of local sensing in higher dimensions. Despite the striking similarity between this system and the Keller--Segel system, we prove the absence of finite-time blow-up phenomenon in…
An initial-Neumann boundary value problem for a Keller--Segel system with density-suppressed motility and source terms is considered. Infinite-time blowup of the classical solution was previously observed for its source-free version when…
In the present article we consider several issues concerning the doubly parabolic Keller-Segel system in the plane, when the initial data belong to critical scaling-invariant Lebesgue spaces. More specifically, we analyze the global…