Asymptotic Profile of Species Migrating on a Growing Habitat |
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Authors: | Qiulin Tang Lai Zhang Zhigui Lin |
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Institution: | (1) Centre for Mathematical Medicine, School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK; |
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Abstract: | This paper deals with a diffusive logistic equation on one dimensional isotropically growing domain. The model equation on
growing domains is first presented, and the comparison principle is then proved. The asymptotic behavior of temporal solutions
to the reaction-diffusion problem is given by constructing upper and lower solutions. Our result shows that when the domain
grows slowly, the species successfully spreads to the whole habitat and stabilizes at a positive steady state, while it dies
out in the long run if the domain grows fast. Numerical simulations are also presented to illustrate the analytical result. |
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Keywords: | |
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