Spatial propagation for a parabolic system with multiple species competing for single resource

Abstract

A model of \begin{document}$m$\end{document} species competing for a single growth-limiting resource is considered. We aim to use the dynamics of such a problem to describe the invasion and spread of \begin{document}$m$\end{document} species which are introduced localized in space \begin{document}$\mathbb{R}^N$\end{document} . The existence, uniqueness and uniform boundedness of the Cauchy problem are investigated by semigroup theory and local \begin{document}$L^p$\end{document} -estimates. The asymptotic speed of spread is achieved by uniform persistence ideas. The existence of traveling wave is obtained by upper-lower solutions and sliding techniques. Our result shows that the asymptotic speed of spread for \begin{document}$m$\end{document} species is characterized by the minimum wave speed of the positive traveling wave solutions associated with this system.