DIFFUSIVE SIZE-STRUCTURED POPULATION MODEL WITH TIME-VARYING DIFFUSION RATE

This work is devoted to the study of a size-structured population model with a time-varying diffusion rate. Due to the seasonal variation, it is natural to consider the time-varying diffusion rate. Moreover, introducing the time-varying diffusion rate makes the model more challenging and requires the results of evolution operators for the analysis. Under some assumptions on the time-dependent diffusion coefficient, the existence and uniqueness of mild solution is shown. We apply the method of characteristics and evolution operators to derive our results. Positivity and boundedness of mild solution is also shown. Some examples are provided to illustrate the theoretical findings. We also solve our model numerically to study the size and spatial dynamics of population density.