相关论文: Generalised global supersolutions with mass contro…

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…

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 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.

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…

In two space dimensions, the parabolic-parabolic Keller--Segel system shares many properties with the parabolic-elliptic Keller--Segel system. In particular, solutions globally exist in both cases as long as their mass is less than 8?.…

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…

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 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.

This paper deals with classical solutions to the parabolic-parabolic system \begin{align*} \begin{cases} u_t=\Delta (\gamma (v) u ) &\mathrm{in}\ \Omega\times(0,\infty), \\[1mm] v_t=\Delta v - v + u &\mathrm{in}\ \Omega\times(0,\infty),…

Unboundedness of solutions is shown to occur in a one-dimensional quasilinear parabolicparabolic chemotaxis system for any initial mass. Our result is also independent of the relation between the speeds of the diffusion of cells and…

We consider a one-dimensional system arising from a chemotaxis model in tumour angiogenesis, which is described by a Keller-Segel equation with singular sensitivity. This hyperbolic-parabolic system is known to allow viscous shocks…

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…

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 a parabolic-parabolic Keller-Segel system of chemotaxis model with singular sensitivity $u_t=\Delta u-\chi\nabla\cdot(\frac{u}{v}\nabla v)$, $v_t=k\Delta v-v+u$ under homogeneous Neumann boundary conditions in a smooth bounded…

This paper is concerned with global solvability of a fully parabolic system of Keller--Segel-type involving non-monotonic signal-dependent motility. First, we prove global existence of classical solutions to our problem with generic…

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…

In this paper we study a semilinear hyperbolic-parabolic system modeling biological phenomena evolving on a network composed by oriented arcs. We prove the existence of global (in time) smooth solutions to this problem. The result is…

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 study the global existence of solutions to the Cauchy problem for the two-dimensional fully parabolic Keller--Segel system at the critical mass. It is known that global-in-time existence holds for initial data with critical mass under…

An Euler-type hyperbolic-parabolic system of chemotactic aggregation describing the vascular network formation is investigated in the critical regularity setting. For small initial data around a constant equilibrium state, the…