### Anisotropic nonlinear elliptic systems with measure data and anisotropic harmonic maps into spheres.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Back to Simple Search
# Advanced Search

This paper deals with the well-posedness in ${L}^{1}\cap {L}^{\mathrm{\infty}}$ 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...

**Page 1**