Stability of semi-wavefronts for delayed reaction-diffusion equations

2017/04/10 by Solar, Abraham
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.03011

Abstract

This paper deals with the asymptotic behavior of solutions to the delayed monostable equation: (*) u_t(t,x) = u_xx(t,x) - u(t,x) + g(u(t-h,x)), x ∈ ℝ, t >0, where h>0 and the reaction term g: ℝ₊ → ℝ₊ has exactly two fixed points (zero and κ>0). Under certain condition on the derivative of g at κ, the global stability of fast wavefronts is proved. Also, the stability of the leading edge of semi-wavefronts for (*) with g satisfying g(u)≤ g'(0)u, u∈\R₊, is established

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