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

Authors
Smith, HL Zhao, XQ
Citation
Hl. Smith et Xq. Zhao, Global asymptotic stability of traveling waves in delayed reaction-diffusion equations, SIAM J MATH, 31(3), 2000, pp. 514-534
Citations number
18
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN journal
00361410 → ACNP
Volume
31
Issue
3
Year of publication
2000
Pages
514 - 534
Database
ISI
SICI code
0036-1410(20000306)31:3<514:GASOTW>2.0.ZU;2-5
Abstract
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 asymp totic stability, Liapunov stability, and uniqueness of traveling wave solut ions are then proved by the elementary super- and subsolution comparison an d squeezing methods.