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We prove convergence of a finite difference scheme to the unique entropy solution of a general form of the Ostrovsky–Hunter equation on a bounded domain with non-homogeneous Dirichlet boundary conditions. Our scheme is an extension of monotone schemes for conservation laws to the equation at hand. The convergence result at the center of this article also proves existence of entropy solutions for the...
We prove the convergence of a finite difference scheme to the unique entropy solution of a general form of the Ostrovsky-Hunter equation on a bounded domain with periodic boundary conditions. The equation models, for example, shallow water waves in a rotating fluid and ultra-short light pulses in optical fibres, and its solutions can develop discontinuities in finite time. Our scheme extends monotone...
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