The Chapman-Enskog procedure for an age-structured population model: initial, boundary and corner layer corrections

We consider a mathematical model of an age-structured population of some fisheries (for example, anchovies, sardines or soles). Two time scales are involved in the problem: the fast time scale for the migration dynamics and the slow time scale for the demographic process. At a first step, we study the so called 'aggregated' system by means of the semigroups theory. Then, we study the asymptotic behaviour of the model by using the Chapman-Enskog procedure. In particular, we study initial, boundary and corner layer effects in order to obtain the exact initial and boundary conditions the approximated solution has to satisfy.