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.


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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[1] Koutsikopoulos, C.; Fortier, L.; Gagne, J.A., Cross-shelf dispersion of dover sole (solea solea) eggs and larvae in biscay bay and recruitment to inshore nurseries, J. plankton res., 13, 923, (1991)
[2] Arino, O.; Koutsikopoulos, C.; Ramzi, A., Element of a model of the evolution of the density of a sole population, J. biol. syst., 4, 445, (1996)
[3] Arino, O.; Sánchez, E.; Bravo De La Parra, R., A model of an age-structured population in a multipatch environment, Math. comput. modell., 27, 4, 137, (1998) · Zbl 1185.35115
[4] Arino, O.; Sánchez, E.; Bravo De La Parra, R.; Auger, P., A singular perturbation in an age-structured population model, SIAM J. appl. math., 50, 2, 408, (1999) · Zbl 0991.92037
[5] Boussouar, A.; Le Bihan, S.; Arino, O.; Prouzet, P., Mathematical model and numerical simulations of the migration and growth of biscay bay anchovy early larval stages, Oceanol. acta, 24, 5, 489, (2001)
[6] Webb, G.F., Theory of nonlinear age-dependent population dynamics, (1985), Marcell Dekker New York · Zbl 0555.92014
[7] Bravo De La Parra, R.; Sánchez, E.; Auger, P., Aggregation methods in population dynamics discrete models, Math. comput. modell., 27, 23, (1998) · Zbl 1185.37185
[8] Kato, T., Perturbation theory for linear operators, (1984), Springer New York
[9] Webb, G.F., An operator-theoretic formulation of asynchronous exponential growth, Trans. am. math. soc., 303, 2, 751, (1987) · Zbl 0654.47021
[10] Mika, J.R.; Banasiak, J., Singularly perturbed evolution equations with applications to kinetic theory, (1995), World Scientific Singapore · Zbl 0948.35500
[11] Frosali, G.; Totaro, S., A scaled nonlinear mathematical model for interaction of algae with light: existence and uniqueness results, Transport theory stat. phys., 26, 1 & 2, 27, (1997) · Zbl 0923.92026
[12] Bravo De La Parra, R.; Arino, O.; Sánchez, E.; Auger, P., A model of an age-structured population with two time scales, Math. comput. modell., 31, 17, (2000) · Zbl 1043.92519
[13] Barletti, L., Some remarks on affine evolution equations with applications to particle transport theory, Math. mod. meth. appl. sci., 10, 6, 877, (2000) · Zbl 1020.34050
[14] Belleni Morante, A., Applied semigroups and evolution equations, (1979), Clarendon Oxford · Zbl 0426.47020
[15] Belleni Morante, A.; Busoni, G., Some remarks on densely defined streaming operators, Math. comput. modell., 21, 8, 13, (1995) · Zbl 0824.47057
[16] ()
[17] Prüß, J., Equilibrium solution of age-specific population dynamics of several species, J. math. biol., 11, 65, (1981) · Zbl 0464.92015
[18] Mokhtar Kharroubi, M., Mathematical topics in neutron transport theory, (1997), World Scientific Singapore · Zbl 0997.82047
[19] Thieme, H.R., Balanced exponential growth for perturbed operator semigroups, Adv. math. sci. appl., 10, 2, 775, (2000) · Zbl 0999.47026
[20] Belleni-Morante, A.; McBride, A.C., Applied nonlinear semigroups, (1998), John Wiley & Sons Chichester · Zbl 0926.47043
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