Asymptotic convergence to pushed wavefronts in a monostable equation with delayed reaction. (19th May 2015)

• Record Type: Journal Article
• Authors: Solar, Abraham; Trofimchuk, Sergei
• Is Part Of: Nonlinearity. Volume 28:Number 7(2015:Jul.)
• Page Start: 2027
• Page End: 2052
• Publication Date: 2015-05-19
• Subjects: pushed wavefront -- monostable -- reaction-diffusion -- spreading speed; 34K12 -- 35K57 -- 92D25; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/28/7/2027
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We study the asymptotic behaviour of solutions to the delayed monostable equation: * with monotone reaction term . Our basic assumption is that this equation possesses pushed traveling fronts. First we prove that the pushed wavefronts are nonlinearly stable with asymptotic phase. Moreover, combinations of these waves attract, uniformly on, every solution of equation (*) with the initial datum sufficiently rapidly decaying at one (or both) infinities of the real line. These results provide a sharp form of the theory of spreading speeds for equation (*).