Nonlinear diffusive-dispersive limits for multidimensional conservation laws

Details Nonlinear diffusive-dispersive limits for multidimensional conservation laws Nonlinear diffusive-dispersive limits for multidimensional conservation laws

2008-10-10

arxiv.org/abs/0810.1880v1

"Advances in nonlinear partial differential equations and related areas'' (Beijing, 1997), pp. 103--123, World Sci. Publ., Riv

Mathematics

Analysis of PDEs

17 pages

Scientific paper

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 establish that the diffusive-dispersive solutions are uniformly bounded in a space Lp ($p$ arbitrary large, depending on the nonlinearity of the diffusion) and converge to the classical, entropy solution of the corresponding multidimensional, hyperbolic conservation law. Previous results were restricted to one-dimensional equations and specific spaces Lp. Our proof is based on DiPerna's uniqueness theorem in the class of entropy measure-valued solutions.

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