| Summary: | 碩士 === 國立中正大學 === 數學系應用數學研究所 === 105 === In this study, we investigate traveling wave solutions in the Producer-Scrounger model proposed by Cosner & Nevai [2]. Previous studies [8] suggest that traveling wave solutions to this model exist only if the associated threshold constant $R_0$ is larger than one. Further, if $R_0>1$, then there exists a critical value $c_m$ such that a traveling wave solution with speed c exists for $c>c_m$, whereas a traveling wave solution with speed c does not exist for $c<c_m$. This leaves open the question whether a traveling wave solution with speed $c_m$ exists. In this study, we give an affirmative answer to this question.
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