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.
Stable upwind schemes for the magnetic induction equation
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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