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Research Article Open access CC BY 3.0

A Result on Global Existence of Solutions to the b-Family of Equations Under Periodic Initial Conditions

Snehanshu Saha

Journal of Advances in Mathematics and Computer Science · pp. 199–208 · Published 23 Oct 2013

10.9734/BJMCS/2014/5495

Abstract

Wave breaking is a phenomenon well-studied in the context of shallow water waves. This paper attempts to connect wave breaking to the global existence of solutions for the periodic peakon b-family of equations. New results on existence of global strong solutions to periodic b-family equations are presented. Periodic initial profile is considered because of strong physical evidence of such behavior of ocean (shallow) waves.

Blow-up b-Family of Equations Local Existence Global Existence

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