相关论文: Multiple peak aggregations for the Keller-Segel sy…
We carry on our studies related to the fully parabolic quasilinear Keller-Segel system started in [6] and continued in [7]. In the above mentioned papers we proved finite-time blowup of radially symmetric solutions to the quasilinear…
In this paper we study the long time asymptotic behavior for a class of diffusion-aggregation equations. Most results except the ones in Section 3.3 concern radial solutions. The main tools used in the paper are maximum-principle type…
We study on the whole space R d the compressible Euler system with damping coupled to the Poisson equation when the damping coefficient tends towards infinity. We first prove a result of global existence for the Euler-Poisson system in the…
We rigorously derive a two-dimensional Keller-Segel type system with signal-dependent sensitivity from a stochastic interacting particle model. By employing suitably defined stopping times, we prove that the convergence of the interacting…
In this paper, we investigate the existence, uniqueness, and exponential decay of asymptotically almost periodic (AAP-) mild solutions for the parabolic-parabolic Keller-Segel systems on a bounded domain $\Omega \subset \mathbb{R}^n$ with a…
We consider a parabolic-elliptic Keller-Segel type system, which is related to a simplified model of chemotaxis. Concerning the maximal range of existence of solutions, there are essentially two kinds of results: either global existence in…
We study the Keller-Segel model of chemotaxis and develop a composite particle-grid numerical method with adaptive time stepping which allows us to accurately resolve singular solutions. The numerical findings (in two dimensions) are then…
We show that the one-dimensional fully parabolic Keller-Segel system with nonlinear diffusion possesses global-in-time solutions, provided the nonlinear diffusion is equal to (1+u)^{-\alpha}, for \alpha < 1, independently on the volume of…
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…
We prove the existence of global-in-time weak solutions to a version of the parabolic-parabolic Keller-Segel system in one spatial dimension. If the coupling of the system is suitably weak, we prove convergence of those solutions to the…
In this paper we consider a one-dimensional fully parabolic quasilinear Keller-Segel system with critical nonlinear diffusion. We show uniform-in-time boundedness of solutions, which means, that unlike in higher dimensions, there is no…
The Keller-Segel partial differential equation is a two-dimensional model for chemotaxis. When the total mass of the initial density is one, it is known to exhibit blow-up in finite time as soon as the sensitivity $\chi$ of bacteria to the…
We consider a system coupling the parabolic-parabolic Keller-Segel equations to the in- compressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up…
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…
We derive two forms of conditional a posteriori error estimates for a finite volume scheme approximating the parabolic-elliptic Keller-Segel system. The estimates control the error in the $L^\infty(0,T, L^2(\Omega))$- and…
We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller--Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero.…
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…
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…
Chemotaxis systems of Keller--Segel type constitute one of the central mathematical frameworks for understanding aggregation phenomena in biological and ecological systems. Over the past decades, the theory has evolved from the classical…
We consider nonnegative radially symmetric solutions of the parabolic-elliptic Keller-Segel system \begin{align*} \left\lbrace \begin{array}{r@{}l@{\quad}l} &u_t=\Delta u-\nabla \cdot \big(u\nabla v\big),\\ &0=\Delta v -\mu + u , \\…