Investigation of the long time dynamics of a diffusive three species aquatic model

Abstract

We consider Upadhay's three species aquatic model with the inclusion of spatial spread. We show the existence of a H2(Ω)×H2(Ω)×H2(Ω) bounded absorbing set in the phase space L2(Ω)×L2(Ω)×L2(Ω). We then derive uniform estimates to tackle the question of asymptotic compactness of the semi-group for the system in the Sobolev space H2(Ω)×H2(Ω)×H2(Ω). Via these we demonstrate the existence of a global attractor for the system which is compact in H2(Ω) and attracts all bounded sets in L2(Ω) in the H2(Ω) topology. © 2010 International Press.