Global existence versus blow up for some models of interacting particles

Piotr Biler (1) , Lorenzo Brandolese (2)

1 Instytut Matematyczny
2 ICJ - Institut Camille Jordan

We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and the Debye-Hukel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and oscillating complex-valued initial data, using a method by S. Montgomery-Smith.

Mots clés: Keller-Segel model; chemotaxis; Debye system; space-time decay; explosion

Domaines: Equations aux dérivées partielles [math.AP]

Piotr Biler, Lorenzo Brandolese. Global existence versus blow up for some models of interacting particles. Colloq. Math., 2006, 106 (2), pp.293--303. ⟨hal-00021903⟩