Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 30, pp. 1-22.
Title: Viscous profiles for traveling waves of scalar balance laws:
The uniformly hyperbolic case
Author: Joerg Haerterich (Freie Univ., Berlin, Germany)
Abstract:
We consider a scalar hyperbolic conservation law with a nonlinear source term
and viscosity $\varepsilon$. For $\varepsilon=0$, there exist in general
different types of heteroclinic entropy traveling waves. It is shown
that for $\varepsilon>0$ sufficiently small the viscous equation possesses
similar traveling wave solutions and that the profiles converge in exponentially
weighted $L^1$-norms as $\varepsilon$ 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.