A singular limit problem for conservation laws related to the Camassa–Holm shallow water equation
G. M. Coclite and K. H. Karlsen
We consider a shallow water equation
of Camassa–Holm type, containing nonlinear dispersive effects
as well as fourth order dissipative effects.
We prove that as the diffusion and dispersion
parameters tend to zero, with a condition on
the relative balance between these two parameters,
smooth solutions of the shallow water equation
converge to discontinuous solutions
of a scalar conservation law. The
proof relies on deriving
suitable a priori estimates together
with an application of the compensated
compactness method in the Lp setting.
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- Giuseppe Maria Coclite,
- Kenneth Hvistendahl Karlsen,
- Publishing information:
- Submitted by:
April 16 2005.
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