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

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

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 fo...

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Veröffentlicht in:Applied mathematics letters 2012-12, Vol.25 (12), p.2317-2321
Hauptverfasser: Huang, Y., Witelski, T.P., Bertozzi, A.L.
Format: Artikel
Sprache:eng
Schlagworte:
Agglomeration
Aggregation equation
Computer simulation
Dynamical systems
Dynamics
Exponents
Finite-time blow-up
Mathematical analysis
Mathematical models
Self-similarity
Self-similarity solution of the second kind
Shooting methods
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Zusammenfassung: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.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2012.06.023