Electron. J. Diff. Eqns., Vol. 2000(2000), No. 30, pp. 122.
Viscous profiles for traveling waves of scalar balance laws:
The uniformly hyperbolic case
Joerg Haerterich
Abstract:
We consider a scalar hyperbolic conservation law with a nonlinear source term
and viscosity
.
For
=0, there exist in general
different types of heteroclinic entropy traveling waves. It is shown
that for
positive and sufficiently small the viscous equation possesses
similar traveling wave solutions and that the profiles converge in
exponentially weighted
norms as
decreases
to zero.
The proof is based on a careful study of the singularly perturbed secondorder
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 26,
D14195 Berlin, Germany
email: haerter@math.fuberlin.de

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