Abstract
The structure of solutions to a simple spatially dependent population model involving growth and death is investigated. Two forms of motility of the population are considered: (1) random motion only modeled by a Fickian law, and (2) a directed component of motion (chemotaxis), included in addition to the random motion. Under certain growth conditions a traveling wave of constant speed is approached. This speed can be increased by the addition of the chemotaxis with a corresponding increase in the asymptotic population. Development of initial conditions into a wave is illustrated numerically.
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Kennedy, C.R., Aris, R. Traveling waves in a simple population model involving growth and death. Bltn Mathcal Biology 42, 397–429 (1980). https://doi.org/10.1007/BF02460793
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DOI: https://doi.org/10.1007/BF02460793