two-dimensional parabolic-elliptic Keller-Segel model

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

We prove some features related to the classical two-dimensional Keller-Segel system: blow-up may or may not occur depending on the initial data.. More precisely a singularity appears

Dans le cas de l’espace ou d’un demi-espace (ou même d’un cône), sous une hypothèse de structure naturelle sur les non-linéarités, nous donnons des conditions suffisantes

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

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

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:

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

In mathematical terms this is expected to correspond to the finite time blow-up of the cell density u near one or several points, along with the formation of one or several