two-dimensional parabolic-elliptic Keller-Segel model

Key words: Keller-Segel model, chemotaxis, drift-di ff usion, self-similar solution, intermediate asymptotics, entropy, free energy, rate of convergence, heat kernel.. 2000 MSC:

By formal asymptotics the dynamics of solutions of the regularized problem is studied under the assumption that in the limit the cell density is the sum of a smooth part and of a

Keller-Segel equations, non compact Riemannian manifolds, negative cur- vature, hyperbolic space, Green function, logarithmic Hardy-Littlewood-Sobolev inequality, entropy

We presented the application of scalar auxiliary variable method to the parabolic-parabolic Keller- Segel with volume filling using the gradient flow structure of the model.. The

Keller-Segel model, Existence, Weak solutions, Free energy, Entropy method, logarithmic Hardy-Littlewood-Sobolev inequality, Critical Mass, Aubin-Lions compactness

The aim of the paper is to prove uniqueness of “free energy” weak solutions to the the so-called parabolic-elliptic Keller-Segel equation in the plane associated to initial datum

In particular, we shall show that the first component of all solutions belonging to a fixed ω − limit set are bounded below away from zero.. In Section 3, we derive some suitable

In this section we apply the previous estimates to prove the existence, local in time, of a weak solution of the parabolic-elliptic Keller-Segel system (1.1).. For simplicity we