Asymptotic behaviour of a reaction–diffusion model with a quiescent stage
- 16 January 2007
- journal article
- research article
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 463 (2080) , 1029-1043
- https://doi.org/10.1098/rspa.2006.1806
Abstract
This paper is devoted to the investigation of the asymptotic behaviour for a reaction–diffusion model with a quiescent stage. We first establish the existence of the asymptotic speed of spread and show that it coincides with the minimal wave speed for monotone travelling waves. Then we obtain a threshold result on the global attractivity of either zero or positive steady state in the case where the spatial domain is bounded.Keywords
This publication has 13 references indexed in Scilit:
- Spreading speeds and traveling waves for periodic evolution systemsJournal of Differential Equations, 2006
- Asymptotic speeds of spread and traveling waves for monotone semiflows with applicationsCommunications on Pure and Applied Mathematics, 2006
- Spreading speeds as slowest wave speeds for cooperative systemsMathematical Biosciences, 2005
- The Effect of Dispersal Patterns on Stream PopulationsSIAM Review, 2005
- Global Attractors and Steady States for Uniformly Persistent Dynamical SystemsSIAM Journal on Mathematical Analysis, 2005
- Saddle-point behavior for monotone semiflows and reaction–diffusion modelsJournal of Differential Equations, 2004
- Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction–diffusion modelsJournal of Differential Equations, 2003
- Analysis of linear determinacy for spread in cooperative modelsJournal of Mathematical Biology, 2002
- Global attractivity and stability in some monotone discrete dynamical systemsBulletin of the Australian Mathematical Society, 1996
- Geometric Theory of Semilinear Parabolic EquationsPublished by Springer Nature ,1981