417 research outputs found
Global solutions for a hyperbolic-parabolic system of chemotaxis
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
Boundedness and homogeneous asymptotics for a fractional logistic Keller-Segel equations
In this paper we consider a -dimensional () parabolic-elliptic
Keller-Segel equation with a logistic forcing and a fractional diffusion of
order . We prove uniform in time boundedness of its solution
in the supercritical range , where is an explicit
constant depending on parameters of our problem. Furthermore, we establish
sufficient conditions for , where
is the only nontrivial homogeneous solution. Finally, we
provide a uniqueness result
Nonlinear Aggregation-Diffusion Equations: Radial Symmetry and Long Time Asymptotics
We analyze under which conditions equilibration between two competing
effects, repulsion modeled by nonlinear diffusion and attraction modeled by
nonlocal interaction, occurs. This balance leads to continuous compactly
supported radially decreasing equilibrium configurations for all masses. All
stationary states with suitable regularity are shown to be radially symmetric
by means of continuous Steiner symmetrization techniques. Calculus of
variations tools allow us to show the existence of global minimizers among
these equilibria. Finally, in the particular case of Newtonian interaction in
two dimensions they lead to uniqueness of equilibria for any given mass up to
translation and to the convergence of solutions of the associated nonlinear
aggregation-diffusion equations towards this unique equilibrium profile up to
translations as
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