| Abstract: |
| In this talk, we report dynamic properties of classical solutions to a homogenous Neumann initial-boundary value problem (IBVP) for a two-species and two-stimuli chemotaxis model with/without chemical signalling loop in a 2D bounded and smooth domain. In radial and elliptic simplification settings, we provide a substantial step toward the (simultaneous) global boundedness and (simultaneous) finite-time blow up. In the general case, i.e., no radial and elliptic simplifications, we successfully detect the product of two species masses as a feature to determine boundedness, gradient estimate, blow-up and W^{j,\infty}( j\geq 1)-exponential convergence of classical solutions for the corresponding IBVP. |
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