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.