Spreading dynamics of a biological invasion model with free boundaries and time delay.

In this paper, we study the global dynamics and asymptotic spreading speed for a biological invasion model with free boundaries and time delay. Given a suitable initial value compatibility condition, the well-posedness of solution is established and some sufficient conditions for spreading and vanishing are derived. Furthermore, by studying an associated semi-wave solution problem, the asymptotic spreading speed for the invasive species is given. It is shown that time delay can slow down the spreading speed. Finally, the dynamics and asymptotic spreading speed are analyzed by numerical simulations. [ABSTRACT FROM AUTHOR]