TITLE

Global solutions and blow-up phenomena for the periodic b-equation

AUTHOR(S)
Zhang, S.; Yin, Z.
PUB. DATE
October 2010
SOURCE
Journal of the London Mathematical Society;Oct2010, Vol. 82 Issue 2, p482
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In the paper, we mainly study the Cauchy problem of a family of asymptotically equivalent shallow water wave equations, the so called periodic b-equation. We first establish the local well-posedness for the periodic b-equation. Then we derive the precise blow-up scenario and present two blow-up results. Moreover, we show that the periodic b-equation has global strong solutions. Finally, we prove the existence of global weak solutions to the periodic b-equation, provided that initial data satisfy certain sign conditions.
ACCESSION #
53882160

 

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