| Abstract: |
| In this talk, we shall investigate a three-species food chain model with taxis mechanisms including prey-taxis and alarm-taxis in a smooth bounded domain with homogeneous Neumann boundary conditions.More precisely, we first establish the boundedness criterion for a general food chain model with various taxis mechanisms for arbitrary spatial dimensions by using the semirgoup estimates and coupled energy estimates. With the boundedness criterion in hand, we use the weighted energy estimates to show the global boundedness of solution for general functional response functions under some smallness assumptions on the taxis coefficients. On the other hand, for some special functional response functions including Beddington-DeAngelis type, ratio-dependent type and Harrison type, we also obtain the global existence of solution with uniform-in-time bound without any smallness assumptions on the taxis coefficients or initial data. |
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