Asymptotic self-similar blow-up for a model of aggregation

Ignacio Guerra. "Asymptotic self-similar blow-up for a model of aggregation." Banach Center Publications 66.1 (2004): 165-188. <http://eudml.org/doc/281665>.

@article{IgnacioGuerra2004,
abstract = {In this article we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the assumptions of radial symmetry, it is known that this system has at least two stable mechanisms of singularity formation (see e.g. M. P. Brenner et al. 1999, Nonlinearity 12, 1071-1098); one type is self-similar, and may be viewed as a trade-off between diffusion and attraction, while in the other type the attraction prevails over the diffusion and a non-self-similar shock wave results. Our main result identifies a class of initial data for which the blow-up behaviour is of the former, self-similar type. The blow-up profile is characterized as belonging to a subset of stationary solutions of the associated ordinary differential equation. We compare these results with blow-up behaviour of related models of aggregation.},
author = {Ignacio Guerra},
journal = {Banach Center Publications},
keywords = {aggregation of particles models; nonlinear nonlocal parabolic system; finite time blow-up},
language = {eng},
number = {1},
pages = {165-188},
title = {Asymptotic self-similar blow-up for a model of aggregation},
url = {http://eudml.org/doc/281665},
volume = {66},
year = {2004},
}

TY - JOUR
AU - Ignacio Guerra
TI - Asymptotic self-similar blow-up for a model of aggregation
JO - Banach Center Publications
PY - 2004
VL - 66
IS - 1
SP - 165
EP - 188
AB - In this article we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the assumptions of radial symmetry, it is known that this system has at least two stable mechanisms of singularity formation (see e.g. M. P. Brenner et al. 1999, Nonlinearity 12, 1071-1098); one type is self-similar, and may be viewed as a trade-off between diffusion and attraction, while in the other type the attraction prevails over the diffusion and a non-self-similar shock wave results. Our main result identifies a class of initial data for which the blow-up behaviour is of the former, self-similar type. The blow-up profile is characterized as belonging to a subset of stationary solutions of the associated ordinary differential equation. We compare these results with blow-up behaviour of related models of aggregation.
LA - eng
KW - aggregation of particles models; nonlinear nonlocal parabolic system; finite time blow-up
UR - http://eudml.org/doc/281665
ER -