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The Chapman – Enskog procedure for an age-structured population model: initial, boundary and corner layer corrections. (English) Zbl 1107.92043
Summary: 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 semigroup 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.

MSC:
92D25 Population dynamics (general)
47D03 Groups and semigroups of linear operators
35Q92 PDEs in connection with biology, chemistry and other natural sciences
47N60 Applications of operator theory in chemistry and life sciences
47F05 General theory of partial differential operators
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