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

100%

Guerra I.

Banach Center Publications

2004

tom 66

nr 1

165-188

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.

Convergence to stationary solutions in a model of self-gravitating systems

63%

Guerra I., Nadzieja T.

Colloquium Mathematicum

2003

tom 98

nr 1

39-47

We study convergence of solutions to stationary states in an astrophysical model of evolution of clouds of self-gravitating particles.

Ograniczanie wyników

1 Banach Center Publications

1 Colloquium Mathematicum

2 Guerra I.

1 Nadzieja T.

1 2004

1 2003

Wyniki wyszukiwania

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

Convergence to stationary solutions in a model of self-gravitating systems