| Abstract: |
| This talk concerns asymptotic regimes of positive steady states in the Shigesada-Kawasaki-Teramoto competition model under large cross diffusion limits. First, we present a systematic classification of limiting regimes according to unilateral or full cross diffusion limits together with boundary conditions including Neumann and Dirichlet cases. We explain how these four settings lead to distinct limiting shadow systems and determine qualitative structures of coexistence states such as segregation, extinction, or concentration profiles. This classification provides a unified framework that organizes previously known results and clarifies structural relations between different limiting procedures. Second, we analyze the unilateral cross diffusion limit with Neumann boundary conditions and describe bifurcation structures of large amplitude steady states near critical spectral thresholds. Combining spectral analysis, singular perturbation techniques, and reduction methods, we establish existence of solution branches and obtain precise descriptions of their asymptotic profiles and instability properties. |
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