Global existence versus blow up for some models of interacting particles

Piotr Biler, and Lorenzo Brandolese. "Global existence versus blow up for some models of interacting particles." Colloquium Mathematicae 106.2 (2006): 293-303. <http://eudml.org/doc/283428>.

@article{PiotrBiler2006,
abstract = {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 Debye-Hückel 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 due to S. Montgomery-Smith.},
author = {Piotr Biler, Lorenzo Brandolese},
journal = {Colloquium Mathematicae},
keywords = {Interacting particles; prabolic systems; solutions global in in time, blow up solutions; non-local semilinear equations; drift diffusion systems; space-periodic solutions},
language = {eng},
number = {2},
pages = {293-303},
title = {Global existence versus blow up for some models of interacting particles},
url = {http://eudml.org/doc/283428},
volume = {106},
year = {2006},
}

TY - JOUR
AU - Piotr Biler
AU - Lorenzo Brandolese
TI - Global existence versus blow up for some models of interacting particles
JO - Colloquium Mathematicae
PY - 2006
VL - 106
IS - 2
SP - 293
EP - 303
AB - 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 Debye-Hückel 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 due to S. Montgomery-Smith.
LA - eng
KW - Interacting particles; prabolic systems; solutions global in in time, blow up solutions; non-local semilinear equations; drift diffusion systems; space-periodic solutions
UR - http://eudml.org/doc/283428
ER -