Multidimensional transition fronts for Fisher–KPP reactions. (8th February 2019)

• Record Type: Journal Article
• Authors: Alwan, Amir; Han, Zonglin; Lin, Jessica; Tao, Zijian; Zlatoš, Andrej
• Is Part Of: Nonlinearity. Volume 32:Number 3(2019)
• Page Start: 927
• Page End: 941
• Publication Date: 2019-02-08
• Subjects: KPP reaction–diffusion equations -- transition solutions with bounded width -- transition fronts; 35K57 -- 35K55; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aaf081
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We study entire solutions to homogeneous reaction–diffusion equations in several dimensions with Fisher–KPP reactions. Any entire solution is known to satisfy and we consider here those satisfying When is and concave, our main result provides an almost complete characterization of transition fronts as well as transition solutions with bounded width within this class of solutions.