Related papers: Global radial solutions in classical Keller-Segel …
We consider the simplest parabolic-elliptic model of chemotaxis in the whole space in several dimensions. Criteria for the blowup of radially symmetric solutions in terms of suitable Morrey spaces norms are derived.
We consider the parabolic-elliptic model for the chemotaxis with fractional (anomalous) diffusion. Global-in-time solutions are constructed under (nearly) optimal assumptions on the size of radial initial data. Moreover, criteria for blowup…
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.…
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…
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…
A simple proof of concentration of mass equal to $8\pi$ for blowing up $N$-symmetric solutions of the Keller--Segel model of chemotaxis in two dimensions with large $N$ is given. Moreover, a criterion for blowup of solutions in terms of the…
We construct radial self-similar solutions of the, so called, minimal parabolic-elliptic Keller--Segel model in several space dimensions with radial, nonnegative initial conditions with are below the Chandrasekhar solution -- the singular…
The existence of generalised global supersolutions with a control upon the total mass is established for a wide family of parabolic-parabolic chemotaxis systems and general integrable initial data in any space dimension. It is verified that…
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 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.…
We consider a class of logarithmic Keller-Segel type systems modeling the spatio-temporal behavior of either chemotactic cells or criminal activities in spatial dimensions two and higher. Under certain assumptions on parameter values and…
In this work we consider the Keller-Segel model for chemotaxis on networks, both in the doubly parabolic case and in the parabolic-elliptic one. Introducing appropriate transition conditions at vertices, we prove the existence of a time…
We study a hyperbolic-parabolic model of chemotaxis in dimensions one and two. In particular, we prove the global existence of classical solutions in certain dissipation regimes.
This paper aims at providing a first step toward a qualitative theory for a new class of chemotaxis models derived from the celebrated Keller-Segel system, with the main novelty being that diffusion is nonlinear with flux delimiter…
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 existence and nonexistence of global in time solutions is studied for a class of equations generalizing the chemotaxis model of Keller and Segel. These equations involve L\'evy diffusion operators and general potential type nonlinear…
We consider a Liouville-type PDE on a smooth bounded planar domain, which is related to stationary solutions of the Keller-Segel's model for chemotaxis. We prove existence of solutions under some algebraic conditions on the parameters. In…
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 chemotaxis system with indirect signal production in the whole space, \begin{equation}\label{abst:p}\tag{$\star$} \begin{cases} u_t = \Delta u - \nabla \cdot (u\nabla v),\\ 0 = \Delta v + w,\\ w_t = \Delta w + u \end{cases}…
In this paper, we investigate global existence of large solutions for the parabolic-elliptic Keller-Segel system in the homogeneous Besov type spaces. A class of initial data was presented, generating a global smooth solution although the…