Geodesic
Viscous profiles for traveling waves of scalar balance laws: The uniformly hyperbolic case
Electronic Journal of Differential Equations, Tome 2000 (2000).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35B25, 35L65, 34C37
Keywords: hyperbolic conservation laws, source terms, traveling waves, viscous profiles, singular perturbations 
@article{EJDE_2000__2000__a187,
     author = {H\"arterich, J\"org},
     title = {Viscous profiles for traveling waves of scalar balance laws: {The} uniformly hyperbolic case},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a187/}
}
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Härterich, Jörg. Viscous profiles for traveling waves of scalar balance laws: The uniformly hyperbolic case. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a187/