We study the limit as __ _* 0 of the eIItropy solutions of the equation Э_tu~Е + diva [x/_ , u~E)] = 0. We prove that the sequence u~6 two-scale converges toward a function u(t, x, y), and u is the unique solution of a limit evolution problem. The remarkable point is that the limit problem is not a scalar conservation law, but rather a kinetic equation in which the macroscopic and microscopic variables are mixed. We also prove a strong convergence result in L_(loc)~1.
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