  It was shown by Schecter (2004, J. Differential Equations, 205, 185-210),
using the methods of Geometric Singular Perturbation Theory, that the Dafermos
regularization $u_t+f(u)_x= \epsilon tu_{xx}$ for the Keyfitz-Kranzer system
admits an unbounded family of solutions. Inspired by that work, in this paper
we provide a more intuitive approach which leads to a stronger result. In
addition to the existence of viscous profiles, we also prove the weak
convergence and show that the maximum of the solution is of order
$\epsilon^{-2}$. This asymptotic behavior is distinct from that obtained in the
author's recent work (arXiv:1512.00394) on a system modeling two-phase fluid
flow, for which the maximum of the viscous solution is of order
$\exp(\epsilon^{-1})$.
