This work provides analytical results towards applications in the field of invasive-invaded systems modeled with nonlinear diffusion and with advection.The results focus on showing regularity,existence and uniqueness ...This work provides analytical results towards applications in the field of invasive-invaded systems modeled with nonlinear diffusion and with advection.The results focus on showing regularity,existence and uniqueness of weak solutions using the condition of a nonlinear slightly positive parabolic operator and the reaction-absorption monotone properties.The coupling in the reaction-absorption terms,that characterizes the species interaction,impedes the formulation of a global comparison principle that is shown to exist locally.Additionally,this work provides analytical solutions obtained as selfsimilar minimal and maximal profiles.A propagating diffusive front is shown to exist until the invaded specie notes the existence of the invasive.When the desertion of the invaded st arts,the diffusive front vanishes globally and the nonlinear diffusion concentrates only on the propagating tail which exhibits finite speed.Finally,the invaded specie is shown to exhibit an exponential decay along a characteristic curve.Such exponential decay is not trivial in the nonlinear diffusion case and confirms that the invasive continues to feed on the invaded during the desertion.展开更多
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This work provides analytical results towards applications in the field of invasive-invaded systems modeled with nonlinear diffusion and with advection.The results focus on showing regularity,existence and uniqueness of weak solutions using the condition of a nonlinear slightly positive parabolic operator and the reaction-absorption monotone properties.The coupling in the reaction-absorption terms,that characterizes the species interaction,impedes the formulation of a global comparison principle that is shown to exist locally.Additionally,this work provides analytical solutions obtained as selfsimilar minimal and maximal profiles.A propagating diffusive front is shown to exist until the invaded specie notes the existence of the invasive.When the desertion of the invaded st arts,the diffusive front vanishes globally and the nonlinear diffusion concentrates only on the propagating tail which exhibits finite speed.Finally,the invaded specie is shown to exhibit an exponential decay along a characteristic curve.Such exponential decay is not trivial in the nonlinear diffusion case and confirms that the invasive continues to feed on the invaded during the desertion.
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.
