Travelling waves for a biological reaction diffusion model with spatio-temporal delay

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:325

Article

Wang, Yifu ; Yin, Jingxue

关键词: travelling wave;    reaction diffusion equations;    singular perturbation;    center manifold theorem;    heteroclinic orbit;   

DOI  :  10.1016/j.jmaa.2006.02.077

来源: Elsevier

【 摘 要 】

In this paper, we consider the reaction diffusion equations with spatio-temporal delay, which models the microbial growth in a flow reactor. Nonlocal spatial term, a weighted average in space, arises when the individuals have not necessarily been at the same point in space at previous time. By employing linear chain technique, geometric singular perturbation, and the center manifold theorem, we prove that the steady travelling wave does not only persist, but also it looks qualitatively the same as it do with no delay at all, under the introduction of delays, at least for small delay. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free