This paper deals with the well-posedness in of the Cauchy problem for the Degasperis-Procesi equation. This is a third order nonlinear dispersive equation in one spatial variable and describes the dynamics of shallow water waves.
We consider the magnetic induction equation for the evolution of a magnetic field in a plasma where the velocity is given. The aim is to design a numerical scheme which also handles the divergence constraint in a suitable manner. We design and analyze an upwind scheme based on the symmetrized version of the equations in the non-conservative form. The scheme is shown to converge to a weak solution of the equations. Furthermore, the discrete divergence produced by the scheme is shown to be...
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