| Abstract: |
| In this talk, we consider a cooperative model with cross-diffusion terms of attractive transition type. In the weak cooperative 3D case, the time global well-posedness of classical non-stationary solutions is shown. Especially in the case of large random diffusion coefficients, we show that any nonstationary positive solution asymptotically approaches the coexistence constant steady state at time infinity by constructing a Lyapunov function. We also discuss the relationship between the bifurcation diagram of the steady states obtained by Adachi-Kuto (2024) and the long-time behavior of the non-stationary solutions. |
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