Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 31, Issue 3, Pages 514-534Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0036141098346785
Keywords
delayed reaction-diffusion equations; comparison principle; super- and subsolutions; traveling waves
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The existence and comparison theorem of solutions is first established for the quasimonotone delayed reaction-diffusion equations on R 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 subsolution comparison and squeezing methods.
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