2020/02/02 by King‐Yeung Lam, Lam, King-Yeung, Rachidi B. Salako +3 · 1 citation
Mathematics · Medicine · #35B08 #35B40 #35K57 #92B05 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.2002.00308
openalex publication_date 2020/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work is concerned with the existence of entire solutions of the diffusive Lotka-Volterra competition system \begincases ut= uxx + u(1-u-av), amp; x∈ℝ \cr vt= d vxx+ rv(1-v-bu), amp; x∈ℝ \endcases (1) where d,r,a, and b are positive constants with a≠ 1 and b≠ 1. We prove the existence of some entire solutions (u(t,x),v(t,x)) of (1) corresponding to (Φc(ξ),0) at t=-∞ (where ξ=x-ct and Φc is a traveling wave solution of the scalar Fisher-KPP defined by the first equation of (1) when a=0). Moreover, we also describe the asymptotic behavior of these entire solutions as t→+∞. We prove existence of new entire solutions for both the weak and strong competition case. In the weak competition case, we prove the existence of a class of entire solutions that forms a 4-dimensional manifold.