Electron. J. Diff. Eqns., Vol. 2000(2000), No. 30, pp. 1-22.

Viscous profiles for traveling waves of scalar balance laws:
The uniformly hyperbolic case

Joerg Haerterich

We consider a scalar hyperbolic conservation law with a nonlinear source term and viscosity $\epsilon$. For $\epsilon$ =0, there exist in general different types of heteroclinic entropy traveling waves. It is shown that for $\epsilon$ positive and sufficiently small the viscous equation possesses similar traveling wave solutions and that the profiles converge in exponentially weighted $L^1$-norms as $\epsilon$ decreases to zero. The proof is based on a careful study of the singularly perturbed second-order equation that arises from the traveling wave ansatz.

Submitted February 22, 2000. Published April 25, 2000.
Math Subject Classifications: 35B25, 35L65, 34C37.
Key Words: Hyperbolic conservation laws, source terms, traveling waves, viscous profiles, singular perturbations.

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Jörg Härterich
Freie Universitat Berlin,
Arnimallee 2-6,
D-14195 Berlin, Germany
e-mail: haerter@math.fu-berlin.de

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