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Preprint 2006-038

A convergent finite difference scheme for the Camassa–Holm equation with general H1 initial data

Giuseppe Maria Coclite, Kenneth Hvistendahl Karlsen and Nils Henrik Risebro

Abstract: We suggest a finite dfference scheme for the Camassa–Holm equation that can handle general H1 initial data. The form of the difference scheme is judiciously chosen to ensure that it satisfies a total energy inequality. We prove that the difference scheme converges strongly in H1 towards an exact dissipative weak solution of Camassa–Holm equation.

Paper:
Available as PDF (512 Kbytes).
Author(s):
Giuseppe Maria Coclite,
Kenneth Hvistendahl Karlsen,
Nils Henrik Risebro,
Publishing information:
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Submitted by:
; 2006-10-25.