Lotka–Volterra competition-diffusion system: the critical competition case. Issue 2 (1st February 2023)

• Record Type: Journal Article
• Authors: Alfaro, Matthieu; Xiao, Dongyuan
• Is Part Of: Communications in partial differential equations. Volume 48:Issue 2(2023)
• Page Start: 182
• Page End: 208
• Publication Date: 2023-02-01
• Subjects: Bump phenomenon -- Cauchy problem -- competition-diffusion system -- large time behavior -- traveling wave; 35K57 (reaction-diffusion equations) -- 35C07 (traveling wave solutions) -- 35B40 (asymptotic behavior of solutions); Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2023.2169936
• Languages: English
• ISSNs: 0360-5302

Abstract

Abstract: We consider the reaction-diffusion competition system in the so-called critical competition case . The associated ODE system then admits infinitely many equilibria, which makes the analysis intricate. We first prove the nonexistence of ultimately monotone traveling waves by applying the phase plane analysis. Next, we study the large time behavior of the solution of the Cauchy problem with a compactly supported initial datum. We not only reveal that the "faster" species excludes the "slower" one (with a known spreading speed ), but also provide a sharp description of the profile of the solution, thus shedding light on a new bump phenomenon .