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

• Autorzy: Ignacio Guerra
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 82C21: Dynamic continuum models (systems of particles, etc.)
• 35K60: Nonlinear initial value problems for linear parabolic equations
• 35B40: Asymptotic behavior of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2004
• Tom: 66
• Numer: 1
• Strony: 165-188

Daty

wydano

2004

Twórcy

autor

Ignacio Guerra

• Centre for Mathematical Modeling, Universidad de Chile, FCFM, Casilla 170 Correo 3, Santiago, Chile

Identyfikatory

DOI

10.4064/bc66-0-11