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 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,
D-14195 Berlin, Germany
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