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Long-time behavior for a regularized scalar conservation law in the absence of genuine nonlinearity. (English) Zbl 0726.35009

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.
Reviewer: K.Zlateva (Russe)

MSC:

35B25 Singular perturbations in context of PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35L65 Hyperbolic conservation laws
35B40 Asymptotic behavior of solutions to PDEs
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