The aim of this work is to provide a formulation of two related nonlinear diffusive convective models in the form of coupled reaction-absorption equations.First,the postulated models are studied with an analytical app...The aim of this work is to provide a formulation of two related nonlinear diffusive convective models in the form of coupled reaction-absorption equations.First,the postulated models are studied with an analytical approach.Later on,numerical evidences are considered to account for a precise characterization.The problem(P)analyzed is of the form:ut=δΔu+c⋅∇u+v^(n),vt=ϵΔv+c⋅∇v−um,n,m∈(0,1),u_(0)(x),v_(0)(x)>0∈L^(1)_(loc)(RN)∩L^(∞)(R^(N)).(0.1)Afterwards,a related problem P_(T)is studied:ut=δΔu+c⋅∇u−v^(n)(u−d),vt=ϵΔv+c⋅∇v−u^(m)v,n,m∈(0,1),u_(0)(x),v_(0)(x)>0∈L^(1)_(loc)(R^(N))∩L^(∞)(R^(N)).(0.2)The principal aspects for analysis are related to the existence and the derivation of particular solutions to reproduce the dynamic of the interacting species.For the problem PT,we make use of the TW approach to study existence of solutions and precise evolution of profiles.Note that the term predator is used to refer to an invasive behavior,while the term prey is used for the invaded species.展开更多
文摘The aim of this work is to provide a formulation of two related nonlinear diffusive convective models in the form of coupled reaction-absorption equations.First,the postulated models are studied with an analytical approach.Later on,numerical evidences are considered to account for a precise characterization.The problem(P)analyzed is of the form:ut=δΔu+c⋅∇u+v^(n),vt=ϵΔv+c⋅∇v−um,n,m∈(0,1),u_(0)(x),v_(0)(x)>0∈L^(1)_(loc)(RN)∩L^(∞)(R^(N)).(0.1)Afterwards,a related problem P_(T)is studied:ut=δΔu+c⋅∇u−v^(n)(u−d),vt=ϵΔv+c⋅∇v−u^(m)v,n,m∈(0,1),u_(0)(x),v_(0)(x)>0∈L^(1)_(loc)(R^(N))∩L^(∞)(R^(N)).(0.2)The principal aspects for analysis are related to the existence and the derivation of particular solutions to reproduce the dynamic of the interacting species.For the problem PT,we make use of the TW approach to study existence of solutions and precise evolution of profiles.Note that the term predator is used to refer to an invasive behavior,while the term prey is used for the invaded species.
