| Contents |
| This talk is concerned with the limiting behavior of the coexistence steady-states to
the Lotka-Volterra competition model as one of the cross-diffusion terms tends to infinity.
Under the Neumann boundary condition, Lou-Ni (1999) derived a couple of shadow systems which characterize the limiting behaviors of the coexistence steady-states. One of the shadow system charcterizing the segregation of the competing species has been studied by Lou-Ni-Yotsutani and the detailed bifurcation structure for the 1D case was revealed.
This talk focuses on the other shadow system characterizing the shrinking of the species not endowed with the cross-diffusion effect. The bifurcation structure of the positive solutions to the shadow system under the Dirichlet/Neumann boundary condition will be stated. |
|