几何分析系列报告之11【穆春来】

Abstract：This work considers a two-species chemotaxis system with Lotka-Volterra competitive kinetic functional response term in a bounded domain with smooth boundary. We proved global bounded solutions to the system in high dimensions without the convexity of the domain. Moreover, by constructing appropriate Lyapunov functionals, it is proved that the solution convergences to the semitrivial steady state under strong competition if the growth coefficients of two species are appropriately large. Furthermore, the linear stability analysis is performed to find the possible patterning regimes, outside the stability parameters regime, for both semi-trivial and coexistence steady states, our numerical simulations show that non-constant steady states and spatially inhomogeneous temporal periodic patterns are all possible.