Electron. J. Diff. Equ., Vol. 2013 (2013), No. 87, pp. 1-11.

Persistence of traveling wave solutions in a bio-reactor model with strong generic delay kernels and nonlocal effect

Nai-Wei Liu, Ting-Ting Kong

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 5, 2013.
Math Subject Classifications: 35K57, 34C37, 92D25.
Key Words: Traveling wave solutions; R-D equations; singular perturbation; strong generic delay kernels; nonlocal effect.

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Nai-Wei Liu
School of Mathematics and Informational Science
Yantai University, Yantai, Shandong 264005, China
email: liunaiwei@yahoo.com.cn
Ting-Ting Kong
School of Mathematics and Informational Science
Yantai University, Yantai, Shandong 264005, China
email: kongtingting1219@gmail.com

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