Traveling curved fronts of bistable Lotka–Volterra competition–diffusion systems in R3. (March 2016)

• Record Type: Journal Article
• Authors: Cao, Meiling; Sheng, Weijie
• Is Part Of: Computers & mathematics with applications. Volume 71:issue 6(2016)
• Page Start: 1270
• Page End: 1286
• Publication Date: 2016-03
• Subjects: Traveling curved fronts -- Lotka–Volterra competition–diffusion systems -- Bistable; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.02.003
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This paper is concerned with the existence and other qualitative properties of three-dimensional traveling curved fronts for bistable Lotka–Volterra competition–diffusion systems in R 3 . It is first shown that there exists a traveling front of convex polyhedral shape to such systems which is asymptotically stable. Then, by taking the limits of such solutions as lateral surfaces go to infinity, one proves the existence as well as the uniqueness of a three-dimensional traveling curved front for any given g ∈ C ∞ ( S 1 ) with min 0 ≤ θ ≤ 2 π g ( θ ) = 0 .