Existence of waves for a reaction–diffusion–dispersion system. (March 2019)

• Record Type: Journal Article
• Authors: Sen, M.; Volpert, V.; Vougalter, V.
• Is Part Of: Nonlinear analysis. Volume 180(2019)
• Page Start: 52
• Page End: 66
• Publication Date: 2019-03
• Subjects: 35K57 -- 35J61 -- 47H11; Travelling waves -- Reaction–diffusion system -- Dispersion; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.09.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Existence of travelling waves is studied for a bistable reaction–diffusion system of equations with linear integral terms (dispersion) and with some conditions on the nonlinearity. The proof is based on the Leray–Schauder method using the topological degree theory for Fredholm and proper operators with the zero index and a priori estimates of solutions in properly chosen weighted spaces.