Global asymptotic stability of traveling waves in delayed reaction–diffusion equations

Key words. Delayed reaction-diffusion equations, comparison principle, super- and sub-solutions, traveling waves. AMS(MOS) Subject Classifications: 35R10, 35B40, 34K30, 58D25. The existence and comparison theorem of solutions is first estab-lished for the quasimonotone delayed reaction-diffusion equations onR by appealing to the theory of abstract functional differential equations. The global asymptotic stability, Liapunov stability and uniqueness of traveling wave solutions are then proved by the elementary super- and sub-solution comparison and squeezing methods