Spreading speeds and monostable waves in a reaction-diffusion model with nonlinear competition
Qiming Zhang (Zhejiang Institute of Meteorological Sciences)
Yazhou Han (China Jiliang University)
Wim T. van Horssen (TU Delft - Mathematical Physics)
Manjun Ma (Zhejiang Institute of Meteorological Sciences)
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Abstract
In this paper the wave propagation dynamics of a Lotka-Volterra type of model with cubic competition is studied. The existence of traveling waves and the uniqueness of spreading speeds are established. It is also shown that the spreading speed is equal to the minimal speed for traveling waves. Furthermore, general conditions for the linear or nonlinear selection of the spreading speed are obtained by using the comparison principle and the decay characteristics for traveling waves. By constructing upper solutions, explicit conditions to determine the linear selection of the spreading speed are derived.