In the first part of this talk, I will introduce some preliminary researches on a non-time-delayed two age structure model in mathematical ecology (in brief, stage structure model). Many variants of this model were first modeled between the late 20th century and the beginning of the 21st century. Also, some studies of parabolic problems have been carried out since early 21st century, for example, classical papers are [1] [2] [3] and the minimum speed of the traveling wave fronts of this class of model was not determined until 2020 by Huang \emph{et al.}

In the rest of this talk, I will introduce a stage-non-stage competitive model (which is also modeled by Prof. Takefumi Nakazawa in NCKU) with a reasonable setting of coefficients to determine which species will win in the same basis of competition. And I will attempt to prove the existence of this three components traveling wave by Schauder fixed-point theorem in weighted Sobolev space and L-infinity space.