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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Global conservative solutions to the Camassa--Holm equation for initial data with nonvanishing asymptotics

Pages: 4209 - 4227, Volume 32, Issue 12, December 2012      doi:10.3934/dcds.2012.32.4209

 
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Katrin Grunert - Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway (email)
Helge Holden - Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway (email)
Xavier Raynaud - Centre of Mathematics for Applications, University of Oslo, NO-0316 Oslo, Norway (email)

Abstract: We show existence of global conservative solutions of the Cauchy problem for the Camassa--Holm equation $u_t-u_{txx}+\kappa u_x+3uu_x-2u_xu_{xx}-uu_{xxx}=0$ with nonvanishing and distinct spatial asymptotics.

Keywords:  Camassa--Holm equation, nonvanishing asymptotics, conservative and global solutions, continuous semigroup.
Mathematics Subject Classification:  Primary: 35Q53, 35B30; Secondary: 35B35, 35D30.

Received: June 2011;      Revised: January 2012;      Available Online: August 2012.

 References