Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 87, pp. 1-11.

Title: Persistence of traveling wave solutions in a bio-reactor model
       with strong generic delay kernels and nonlocal effect
        
Authors: Nai-Wei Liu    (Yantai Univ., Shandong, China)
         Ting-Ting Kong (Yantai Univ., Shandong, China)

Abstract:
 In this article, we consider the persistence of nontrivial
 traveling wave solutions of a bio-reactor system with
 strong generic delay kernels and nonlocal effect, which models the
 microbial growth in a flow reactor. By using the geometric singular
 perturbation theory and the center manifold theorem, we show that
 traveling wave solutions exist provided that the delays are
 sufficiently small with the strong generic delay kernels.

Submitted February 24, 2013. Published April 05, 2013.
Math Subject Classifications: 35K57, 34C37, 92D25.
Key Words: Traveling wave solutions; R-D equations; singular perturbation;
           strong generic delay kernels; nonlocal effect.