±¨¸æÕªÒª£ºThis talk is concerned with a Lotka-Volterra model with nonlinear cross diffusion. The global existence of generalized solutions is established under some proper assumptions, and the nonexistence of non-constant solutions is also investigated when diffusion rate is sufficiently large. At the same time, sufficient conditions ensuring the existence of non-constant solutions are obtained by using Leray-Schauder degree theory. Furthermore, steady-state bifurcation analysis is carried out in details by using Lyapunov-Schmidt reduction.. This is a joint work with my PhD student Changfeng Liu at HNU.
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