Free boundary problems for the local-nonlocal diffusive model with different moving parameters

Abstract

<p style='text-indent:20px;'>This paper concerns a class of local and nonlocal diffusion systems with double free boundaries possessing different moving parameters. We firstly obtain the existence, uniqueness and regularity of global solution and then prove that its dynamics are governed by a spreading-vanishing dichotomy. Then the sharp criteria for spreading and vanishing are established. Of particular importance is that long-time behaviors of solution in this problem are quite rich under the Lotka-Volterra type competition, prey-predator and mutualist growth conditions. Moreover, we also provide rough estimates of spreading speeds when spreading happens.</p>