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June  2010, 3(2): 299-309. doi: 10.3934/krm.2010.3.299

A mean-field toy model for resonant transport

Patrick Gerard 1, and  Christophe Pallard 1,

1. 

Université Paris-Sud XI, Laboratoire de Mathématiques, 91405 Orsay Cedex, France, France

Received  September 2009 Revised  November 2009 Published  May 2010

We consider a simple one dimensional mean-field equation modeling a resonant setting in a coupled wave + transport system. Using elementary methods, we obtain sufficient conditions on the initial data to ensure global existence or blow-up in finite time.
Keywords: blow-up., smooth solutions, Vlasov-Maxwell system, resonant coupling.
Mathematics Subject Classification: Primary: 35Q83, 35B40; Secondary: 82D1.
Citation: Patrick Gerard, Christophe Pallard. A mean-field toy model for resonant transport. Kinetic and Related Models, 2010, 3 (2) : 299-309. doi: 10.3934/krm.2010.3.299
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