Competitive reversals inside ecological reserves: The role of external habitat degradation (Q1272526)

The authors study a model describing external habitat degradation. It leads to a single species model of logistic form with diffusion or to a diffusive Lotka-Volterra competition model. The boundary conditions are of Robin type. The main mathematical problem they study is the elliptic system: \[ -\Delta \varphi_1+ \beta_1u_2(x) \varphi_1= \alpha_1\varphi_1, \quad-\Delta \varphi_2+ \beta_2u_1(x) \varphi_2= \alpha_2\varphi_1, \quad\text{in }\Omega, \] \[ \partial \varphi_1/ \partial n+\gamma_1 \varphi_1=0, \quad\partial \varphi_2/ \partial n+\gamma_2 \varphi_2=0, \quad\text{on }\partial \Omega. \] Here \(u_1(x)\), \(u_2(x)\) are steady states of the related scalar problems. They give a thorough study of how the parameters affect the solution together with biological interpretations.