Abstract: We study the question whether some traveling waves of a scalar balance law $u_t + f(u)_x =g(u)$ can be approximated by traveling waves of the viscous regularization $u_t + f(u)_x= \varepsilon u_{xx}+g(u)$ such that the wave speed of the viscous traveling waves tends to the wave speed of the hyperbolic traveling wave as $\varepsilon$ tends to zero. Also we require the profiles to converge in $L^1$. Using a blow-up method from geometrical singular perturbation theory we give a positive result for the monotone traveling waves which occur at isolated wave speeds.
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