Long-time behavior for a regularized scalar conservation law in the absence of genuine nonlinearity (Q802848)

The regularized conservation law (1) \(u_ t+(\phi (u))_ x=\epsilon (a(u)u_ x)_ x\) with a(u) strictly positive and \(\phi\) (u) not necessarily convex is studied. It is shown that as time approaches infinity, the solution of (1) converges along rays to the solution of a certain Riemann problem for the hyperbolic conservation law, even when this conservation law is not genuinely nonlinear.