| Abstract: |
| We are interested in SKT cross-diffusion equation. The equation is proposed by Shigesada, Kawasaki and Teramoto in 1979 to investigate segregation phenomena of two competing species with each other in the same habitat area. The effect of cross-diffusion affects the population pressure between two different kinds. Lou and Ni derived limiting equations to see whether this effect may give rise to a spatial segregation or not, and to clarify its mechanism. In this talk, we introduce a new representation of solutions to a stationary limiting problem modified from representation by Lou, Ni and Yotsutani. Moreover, we show existence, nonexistence, multiplicity, and numerical stability of stationary solutions for the limiting equation by analyzing the representation. This is joint work with Y. Lou, H. Matsubara, W.-M. Ni, S. Sukekuni and S. Yotsutani. |
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