| Abstract: |
| In this talk, we will report our recent research results on a diffusive predator-prey model with a free boundary in a radially symmetric setting, which arises in a biological invasion problem. The spreading-vanishing dichotomy is obtained for this model, and sharp criteria for spreading and vanishing are given. The numerical simulations reveal that the average speed of the free boundary varies linearly over large rang, which inspires us to consider semi-wave solutions of the same system and establish the existence and uniqueness of such solution. Our result shows that the asymptotic spreading speed of invasion species in the free boundary problem is no more than the asymptotic spreading speed of the Cauchy problem associated with this system. |
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