A Fisher-KPP model with a fast diffusion line in a periodic medium

In this thesis, we present the road-field model with a different reaction term. We take f depending on the density of population v and depending periodically on the variable space y, and we take weaker hypotheses on f. Some similar hypotheses can be found in the model by Berestycki, Hamel and Roques [3], that studies a reactiondi diffusion process in a periodic medium, but has no faster diffusion line. The model we investigate combine the interest in the effects of a transportation network with the need to have a heterogeneous medium, reecting the natural environment [13]. Many of the proofs that we are presenting in this work are combinations and adaptations of the ideas of the three papers [6, 7, 3].