Qualitative studies of Lotka-Volterra competition system with advection


Qi Wang

11:20:00 - 12:10:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, we consider a diffusive Lotka-Volterra competition system with advection under Neumann boundary conditions. Our model describes a relationship that one species escape from the region of high population density of inter-specific competitors in order to avoid competition. The global existence of bounded classical solutions are established for a parabolic-parabolic system over one-dimensional domains and for its parabolic-elliptic counterpart over multi-dimensional domains. We then study the existence and stability of non-constant positive steady states through bifurcation theories. As the diffusion and advection rate of the first competitor go to infinity, it is shown that this reaction-advection-diffusion system converges to a shadow system when . We construct positive solutions with an interior transition layer to the shadow system at any predetermined point over the given interval. Numerical simulations are presented to illustrate and support our theoretical results.

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