The hair-trigger effect for a class of nonlocal nonlinear equations. (20th April 2018)

• Record Type: Journal Article
• Authors: Finkelshtein, Dmitri; Tkachov, Pasha
• Is Part Of: Nonlinearity. Volume 31:Number 6(2018:Jun.)
• Page Start: 2442
• Page End: 2479
• Publication Date: 2018-04-20
• Subjects: hair-trigger effect -- nonlocal diffusion -- reaction–diffusion equation -- monostable equation -- long-time behaviour -- integral equation -- nonlocal nonlinearity; 35B40 -- 35K57 -- 47G20 -- 45G10; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aab1cb
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We prove the hair-trigger effect for a class of nonlocal nonlinear evolution equations on which have only two constant stationary solutions, 0 and . The effect consists in that the solution with an initial condition non identical to zero converges (when time goes to ) to θ locally uniformly in . We also find sufficient conditions for existence, uniqueness and comparison principle in the considered equations.