Free boundary problems for the diffusive competition system in higher dimension with sign-changing coefficients

Abstract

Abstract. In this article we investigate two free boundary problems for a LotkaVolterra competition system in a higher space dimension with sign-changing coefficients. One may be viewed as describing how two competing species invade if they occupy an initial region, the other describes the dynamical process of a new competitor invading into the habitat of a native species. For simplicity, it is assumed that the environment is radially symmetric. The main purpose of this article is to understand the asymptotic behavior of competing species spreading via a free boundary. We derive some sufficient conditions for species spreading success and spreading failure. Moreover, when spreading successfully, we provide the long time behavior of solutions.

The diffusive Beddington‐DeAngelis predator‐prey model with nonlinear prey‐taxis and free boundary

“…Proof. In view of (10), (30), and assumption h ∞ < ∞, it is easy to derive that lim t→∞ h ′ (t) = 0.…”

A free boundary problem for an attraction–repulsion chemotaxis system

“…To the best of our knowledge, this is the first work concerning the free boundary problem of chemotaxis systems. Other works for various species competition systems with free boundaries can be found in [8,10,12,13,40,47,49]. The authors of [11,18,19,30] considered the transmission of viruses and diseases by using a free boundary.…”

Free boundary problems with nonlocal and local diffusions I: Global solution

“…However, from [19, Remark 1.4] we know that when d ≤ f ′ (0), spreading happens no matter how small h 0 , µ and u 0 are. This is very different from the spreading-vanishing criteria for the local diffusion models.Motivated by the papers [19] and [1,2,8,9,20] (two species local diffusion systems with common free boundary), the authors of [4] studied the following free boundary problem of nonlocal diffusive…”