A reaction-diffusion-advection competition model with two free boundaries in heterogeneous time-periodic environment

In this article, westudy the dynamics of a two-species competition model with two different free boundaries in heterogeneous time- periodic environment, where the two species adopt a combination of random movement and advection upward along the resource gradient. We show that the dynamics of this model can be classified into four cases, which form a spreading-vanishing quartering. The notion of the minimal habitat size for spreading is introduced to determine if species can always spread. Rough estimates of the asymptotic spreading speed of free boundaries and the long-time behaviour of solutions are also established when spreading occurs. Furthermore, some sufficient conditions for spreading and vanishing are provided.