Mathematics – Analysis of PDEs
Scientific paper
2004-04-15
Mathematics
Analysis of PDEs
28 pages, 1 figure with 2 pictures
Scientific paper
10.1088/0951-7715/17/6/007
In this paper 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.
Guerra Ignacio A.
Peletier Mark A.
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