Travelling waves for a biological reaction diffusion model with spatio-temporal delay |
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Authors: | Yifu Wang Jingxue Yin |
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Institution: | a Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China b Department of Mathematics, Jilin University, Changchun, Jilin 130012, China |
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Abstract: | 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. |
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Keywords: | Travelling wave Reaction diffusion equations Singular perturbation Center manifold theorem Heteroclinic orbit |
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