Abstract
We study the large time asymptotic behavior of solutions of the Cauchy problem for the viscous scalar conservation laws. If there exists a travelling wave solution, then it is well known that solutions of the Cauchy problem converge to it. In the case where a wave does not exist we introduce a notion of system of waves, which is a set of waves propagating with different velocities. We show that solutions of the Cauchy problem converge to the system of waves.
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