Related papers: A global existence result for a Keller-Segel type …
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 study the existence of global solutions to semilinear wave equations on exterior domains $\mathbb{R}^n\setminus\mathcal{K}$, $n\geq2$, with small initial data and nonlinear terms $F(\partial u)$ where $F\in C^\kappa$ and…
A finite volume scheme for the (Patlak-) Keller-Segel model in two space dimensions with an additional cross-diffusion term in the elliptic equation for the chemical signal is analyzed. The main feature of the model is that there exists a…
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…
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 article deals with the logistic Keller-Segel model \[ \begin{cases} u_t = \Delta u - \chi \nabla\cdot(u\nabla v) + \kappa u - \mu u^2, \\ \\ v_t = \Delta v - v + u \end{cases} \] in bounded two-dimensional domains (with homogeneous…
We obtain global existence results for the Cauchy problem associated to the Schrodinger-Debye system for a class of data with infinite mass (L2-norm). A smallness condition on data is assumed. Our results include data such as…
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,…
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 study the controllability of the Keller-Segel system approximating its parabolic-elliptic version. We show that this parabolic system is locally uniform controllable around a constant solution of the parabolic-elliptic…
We consider the Cauchy problem for the Keller-Segel system of consumption type coupled with the incompressible Euler equations in $\mathbb{R}^2$. This coupled system describes a biological phenomenon in which aerobic bacteria living in…
\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}…
Under a natural stability condition on the pressure, it is known that for small irrotational initial data, the solutions of the Euler-Korteweg system are global in time. When the initial velocity has a small rotational part, we obtain a…
This work is devoted to the study of the initial boundary value problem for a general isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985), which can be used as a phase transition model. We will prove the existence…
Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it…
The present paper deals with the parabolic-parabolic Keller-Segel equation in the plane inthe general framework of weak (or "free energy") solutions associated to an initial datum with finite mass $M\textless{} 8\pi$, finite second…
This paper is concerned with global existence as well as infinite-time blowups of classical solutions to the following fully parabolic kinetic system \begin{equation} \begin{cases} u_t=\Delta (\gamma (v)u) v_t-\Delta v+v=u \end{cases}…
The flux-limited Keller--Segel system \begin{align*} \begin{cases} u_t = \Delta u - \chi \nabla \cdot (u|\nabla v|^{p-2}\nabla v), \\[] v_t = \Delta v - v + u^{\theta} \end{cases} \end{align*} is considered under homogeneous Neumann…
In this paper, we establish the existence and uniqueness of solutions of elliptic-parabolic stochastic Keller-Segel systems. The solution is obtained through a carefully designed localization procedure together with some a priori estimates.…
We study global-in-time well-posedness and the behaviour and of the solution to Cauchy problem in the classical Keller-Segel system with logistic term \begin{equation*} \left. \aligned \partial_tn-\Delta n=&-\chi\nabla\cdot(n\nabla c)+\la…