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Bounded Solutions for the Degasperis-Procesi Equation

Giuseppe Maria Coclite; Kenneth H. Karlsen — 2008

Bollettino dell'Unione Matematica Italiana

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

Stable upwind schemes for the magnetic induction equation

Franz G. Fuchs; Kenneth H. Karlsen; Siddharta Mishra; Nils H. Risebro — 2009

ESAIM: Mathematical Modelling and Numerical Analysis

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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Currently displaying 1 – 6 of 6

Bounded Solutions for the Degasperis-Procesi Equation

Stable upwind schemes for the magnetic induction equation

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

Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations.

On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient.

On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations.