SYMMETRIZATION AND ENTROPY INEQUALITY FOR GENERAL DIFFUSION-EQUATIONS

Starting from an arbitrary system of diffusion equations, a compatibil ity condition for a convex function is given to be an entropy associat ed with this system. It is shown that if such an entropy exists, then a symmetric formulation of the diffusion system exists. Conversely, if a symmetric formulation exists, then an entropy exists. Besides, some systems of diffusion equations can be derivated from a kinetic equati on. The link between entropy, symmetric formulation, and kinetic level is investigated.