A Leslie-Gower predator-prey model with a two-free boundary

In this article, we study the behavior of two species evolving in a domain with a two-free boundary. This system mimics the spread of invasive or new predator species, in which free boundaries represent the expanding fronts of predator species and are described by the Stefan condition. A priori estimates for the required functions are established. These estimates are used to prove the existence and uniqueness of the solution.