相关论文: Global well-posedness of logarithmic Keller-Segel …
We study a Keller-Segel type chemotaxis model with a modified sensitivity function in a bounded domain $\Omega\subset \mathbb{R}^N$, $N\geq2$. The global existence of classical solutions to the fully parabolic system is established provided…
The existence of generalised global supersolutions with a control upon the total muss is established for the parabolic-parabolic Keller-Segel system with logarithmic sensitivity for any space dimension. It is verified that smooth…
We consider a nonlinear, strongly coupled, parabolic system arising in the modeling of burglary in residential areas. The system is of chemotaxis-type and involves a logarithmic sensivity function and specific interaction and relaxation…
The Keller-Segel model is a system of partial differential equations modelling chemotactic aggregation in cellular systems. This model has blowing up solutions for large enough initial conditions in dimensions d >= 2, but all the solutions…
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…
We consider the simplest parabolic-elliptic model of chemotaxis in the whole space in several dimensions. Criteria for the existence of radial global-in-time solutions in terms of suitable Morrey norms are derived.
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…
The chemotaxis system \[ \left\{ \begin{array}{l} u_t = \Delta u - \chi\nabla \cdot (\frac{u}{v}\nabla v), v_t=\Delta v - v+u, \end{array} \right. \] is considered in a bounded domain $\Omega\subset \mathbb{R}^n$ with smooth boundary, where…
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…
In this paper, we study the global stability of classical solutions to a Keller--Segel equations in scaling-invariant spaces. We prove that for any given $0<\mathcal{M}<1+\lambda_1$ with $\lambda_1$ being the first eigenvalue of Neumann…
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 consider the Keller-Segel model of chemotaxis on one-dimensional networks. Using a variational characterization of solutions, positivity preservation, conservation of mass, and energy estimates, we establish global existence of weak…
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 the two-species Keller--Segel-Stokes system with competitive kinetics $(n_1)_t + u\cdot\nabla n_1 =\Delta n_1 - \chi_1\nabla\cdot(n_1\nabla c)+ \mu_1n_1(1- n_1 - a_1n_2)$, $(n_2)_t + u\cdot\nabla n_2 =\Delta n_2 -…
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…
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…
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…
A Keller-Segel model describes macroscopic dynamics of bacterial colonies and biological cells. Bacteria secret chemical which attracts other bacteria so that they move towards chemical gradient creating nonlocal attraction between…
In this paper, we study global well-posedness of the two-dimensional Keller-Segel model in Lebesgue space and Sobolev space. Recall that in the paper "Existence and uniqueness theorem on mild solutions to the Keller-Segel system in the…
We study a new nonlocal approach to the mathematical modelling of the Chemotaxis problem, which describes the random motion of a certain population due a substance concentration. Considering the initial-boundary value problem for the…