AICME II abstracts
Mathematical modeling and computer simulations...
Mathematical modeling and computer simulations...
A mathematical study for a quasilinear model of size-structured populations O.Arino
1
, S. Boulite2 , Hammadi Bouslous3 and My Lhassan Hbid4 .
In this work, we study the existance and some regularty propertise of the solution of the following quasilinear size-structured model with competition effect between individuals of different sizes ∂ + ∂s ([f (s) + 0s L(s, v)u(v, t)dv]u(s, t)) = −µ(s)u(s, t), R +∞ 0 u(0, t) = 0 β(s)u(s, t)ds, t ≥ t1 , u(·, t ) = ϕ. 1
∂u ∂t (s, t)
R
t ≥ t1 , s ≥ 0,
u(s, t) represents the density of population with size s at time t, we include here population with several species. µ(·) and β(·) are respectively the mortality and the fertility rates. f0 (s) is the minimal growth of the biomass of the population with size s and L(·, ·) represents the kernel of intra and inter-specific competition.
References [1] O.Arino, Chr. Mullon, Y. Shin and Ph. Cury. Etude math´ematique d’un mod`ele de croissance de la biomasse sous l’hypoth`ese de pr´edation des moins gros par les plus gros. Preprint. 1 Institut de Recherche pour le Dveloppement (IRD), 32 avenue Henri Varagnat, F-93143 Bondy, France (e-mail:
[email protected]). 2 Facult´e des Sciences Semlalia D´epartement de Math´ematiques, BP 2390, Marrakesh, Morocco (e-mail:
[email protected]). 3 Facult´e des Sciences Semlalia D´epartement de Math´ematiques, BP 2390, Marrakesh, Morocco (e-mail:
[email protected]). 4 Facult´e des Sciences Semlalia D´epartement de Math´ematiques, BP 2390, Marrakesh, Morocco (e-mail:
[email protected]).
12-Ari-a
12-Ari-b
AICME II abstracts
