This article is concerned with a population dynamic model with delay and quiescent stage. By using the weighted-energy method combining continuation method, the exponential stability of traveling waves of the model un...This article is concerned with a population dynamic model with delay and quiescent stage. By using the weighted-energy method combining continuation method, the exponential stability of traveling waves of the model under non-quasi-monotonicity conditions is established. Particularly, the requirement for initial perturbation is weaker and it is uniformly bounded only at x = ＋∞ but may not be vanishing.展开更多
By using the weighted-energy method combining continuation method, the exponential stability of monostable traveling waves for a delayed equation without quasimonotonicity is established, including even the slower wav...By using the weighted-energy method combining continuation method, the exponential stability of monostable traveling waves for a delayed equation without quasimonotonicity is established, including even the slower waves whose speed are close to the critical speed. Particularly, the nonlinearity is nonlocal in the equation and the initial perturbation is uniformly bounded only at x=+∞ but may not be vanishing.展开更多
The stability of traveling wavefronts for a spatially nonlocal population model with quasi-monotonicity and delay is discussed in this article.It is shown that all monostable wavefronts are exponentially stable for la...The stability of traveling wavefronts for a spatially nonlocal population model with quasi-monotonicity and delay is discussed in this article.It is shown that all monostable wavefronts are exponentially stable for large speed with the help of weightedenergy method and comparison principle.The proper selection of the weighted function is necessary to overcome the difficulty caused by the nonlocal nonlinearity for establishing the energy estimates of solutions.展开更多
基金supported by the NSF of China(11761046,11301241)
文摘This article is concerned with a population dynamic model with delay and quiescent stage. By using the weighted-energy method combining continuation method, the exponential stability of traveling waves of the model under non-quasi-monotonicity conditions is established. Particularly, the requirement for initial perturbation is weaker and it is uniformly bounded only at x = ＋∞ but may not be vanishing.
文摘By using the weighted-energy method combining continuation method, the exponential stability of monostable traveling waves for a delayed equation without quasimonotonicity is established, including even the slower waves whose speed are close to the critical speed. Particularly, the nonlinearity is nonlocal in the equation and the initial perturbation is uniformly bounded only at x=+∞ but may not be vanishing.
基金Supported by the NSF of China(Grant No.11761046)Science and Technology Plan Foundation of Gansu Province of China(Grant No.20JR5RA411)Foundation of A Hundred Youth Talents Training Program of Lanzhou Jiaotong University.
文摘The stability of traveling wavefronts for a spatially nonlocal population model with quasi-monotonicity and delay is discussed in this article.It is shown that all monostable wavefronts are exponentially stable for large speed with the help of weightedenergy method and comparison principle.The proper selection of the weighted function is necessary to overcome the difficulty caused by the nonlocal nonlinearity for establishing the energy estimates of solutions.
