Elsevier

Applied Mathematics Letters

Volume 25, Issue 12, December 2012, Pages 2317-2321
Applied Mathematics Letters

Anomalous exponents of self-similar blow-up solutions to an aggregation equation in odd dimensions

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Abstract

We calculate the scaling behavior of the second-kind self-similar blow-up solution of an aggregation equation in odd dimensions. This solution describes the radially symmetric finite-time blowup phenomena and has been observed in numerical simulations of the dynamic problem. The nonlocal equation for the self-similar profile is transformed into a system of ODEs that is solved using a shooting method. The anomalous exponents are then retrieved from this transformed system.

Keywords

Aggregation equation
Self-similarity solution of the second kind
Finite-time blow-up
Shooting methods

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