Per citar aquest document: http://ddd.uab.cat/record/50347
Semigroup analysis of structured populations with distributed states-at-birth arising in mathematical aquaculture
Farkas, József Z.
Green, Darren
Hinow, Peter
Centre de Recerca Matemàtica

Publicació: Centre de Recerca Matemàtica 2009
Descripció: 21 p.
Col·lecció: Prepublicacions del Centre de Recerca Matemàtica ; 865
Resum: Motivated by the modelling of structured parasite populations in aquaculture we consider a class of physiologically structured population models, where individuals may be recruited into the population at different sizes in general. That is, we consider a size-structured population model with distributed states-at-birth. The mathematical model which describes the evolution of such a population is a first order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In case of a separable fertility function we deduce a characteristic equation and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.
Drets: Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús Creative Commons
Llengua: Anglès.
Document: preprint
Matèria: Estabilitat ; Teoria espectral (Matemàtica) ; Semigrups ; Aqüicultura

Adreça alternativa: http://hdl.handle.net/2072/41797


21 p, 232.0 KB

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