Nonlinear estimates for traveling wave solutions of reaction diffusion equations

2019/07/12 by Li-Chang Hung, Hung, Li-Chang, Xian Liao +1
Mathematics · Medicine · #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.1907.05821

openalex publication_date 2019/07/12 · openalex created_date 2019/07/23 · openalex updated_date 2026/07/28

Abstract

In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction-diffusion equations, and we will apply our nonlinear bounds to the Lotka-Volterra system of two competing species as examples. The idea used in a series of papers \citeNBMP-Discrete,JDE-16,CPAA-16,DCDS-B-18,NBMP-n-species,DCDS-A-17 for the establishment of the linear N-barrier maximum principle will also be used in the proof.

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