Global Asymptotic Stability of Traveling Waves in Delayed Reaction-Diffusion Equations
Top Cited Papers
- 1 January 2000
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 31 (3) , 514-534
- https://doi.org/10.1137/s0036141098346785
Abstract
The existence and comparison theorem of solutions is first established for the quasi-monotone 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.Keywords
This publication has 12 references indexed in Scilit:
- Monotonicity and convergence results in order-preserving systems in the presence of symmetryDiscrete & Continuous Dynamical Systems, 1999
- Global Asymptotics in Some Quasimonotone Reaction-Diffusion Systems with DelaysJournal of Differential Equations, 1997
- Global Stability of Traveling Fronts and Convergence Towards Stacked Families of Waves in Monotone Parabolic SystemsSIAM Journal on Mathematical Analysis, 1996
- Theory and Applications of Partial Functional Differential EquationsPublished by Springer Nature ,1996
- Traveling Wave Solutions of Parabolic SystemsPublished by American Mathematical Society (AMS) ,1994
- Stability and Oscillations in Delay Differential Equations of Population DynamicsPublished by Springer Nature ,1992
- Differential equation models of some parasitic infections: Methods for the study of asymptotic behaviorCommunications on Pure and Applied Mathematics, 1985
- Semigroups of Linear Operators and Applications to Partial Differential EquationsPublished by Springer Nature ,1983
- The approach of solutions of nonlinear diffusion equations to travelling front solutionsArchive for Rational Mechanics and Analysis, 1977
- Existence and stability for partial functional differential equationsTransactions of the American Mathematical Society, 1974