A Result on Global Existence of Solutions to the b-Family of Equations Under Periodic Initial Conditions
Snehanshu Saha *
Department of Computer Science & Center for Bio-Inspired and Evolutionery computation,Simulation and Applications(CBECSA) PESIT South Campus, Bangalore Karnataka, India.
*Author to whom correspondence should be addressed.
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.
Keywords: Blow-up, b-Family of Equations, Local Existence, Global Existence