On Vanishing dissipative-dispersive perturbations of hyperbolic conservation laws

Abstract

In presence of linear diffusion and non-positive dispersion, we prove well-posedness of the nonlinear conservation equation u_t+f(u)_x=\eps u_xx -\del((u_xx)^2)_x. Then, as the right-hand perturbations vanish, we prove convergence of the previous solutions to the entropy weak solution of the hyperbolic conservation law u_t+f(u)_x=0.