Paramétrices microlocales de problèmes aux limites pour une classe d'équations pseudo-différentielles à caractéristiques de multiplicité variable
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources in population dynamics. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. They can be related to the emergence of biological species due to the intra-specific competition and random mutations. Various types of travelling waves are observed.