Abstract
We consider a class of multidimensional conservation laws with vanishing nonlinear diffusion and dispersion terms. Under a condition on the relative size of the diffusion and dispersion coefficients, we show that the approximate solutions converge in a strong topology to the entropy solution of a scalar conservation law. Our proof is based on methodology developed in [S. Hwang, A.E. Tzavaras, Kinetic decomposition of approximate solutions to conservation laws: Applications to relaxation and diffusion–dispersion approximations, Comm. Partial Differential Equations 27 (2002) 1229–1254] which uses the averaging lemma.
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