Abstract:We prove that a certain finite difference scheme converges to the weak solution of the Cauchy problem on a finite interval with periodic boundary conditions for the Camassa–Holm equationu_{t}-u_{xxt}+3uu_{x}-2u_{x}u_{xx}-uu_{xxx}=0 with initial datau|_{t=0}=u_{0}∈H^{1}([0,1]). Here it is assumed thatu-u_{0}''≥0 and in this case, the solution is unique, globally defined, and energy preserving.

**Paper:**- Available as PDF (360 Kbytes), Postscript (1368 Kbytes) or gzipped PostScript (464 Kbytes; uncompress using gunzip).
**Author(s):**- Helge Holden, <holden@math.ntnu.no>
- Xavier Raynaud, <raynaud@math.ntnu.no>
**Publishing information:****Comments:****Submitted by:**- <holden@math.ntnu.no> July 22 2004.

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Conservation Laws Preprint Server <conservation@math.ntnu.no> 2004-07-22 13:07:16 UTC