In this paper,we study the linear determinacy of the minimal speed of traveling wave-fronts for a three-component competition system with nonlocal dispersal.We first trans-form this system into a cooperative system.Th...In this paper,we study the linear determinacy of the minimal speed of traveling wave-fronts for a three-component competition system with nonlocal dispersal.We first trans-form this system into a cooperative system.Then,by constructing suitable upper solu-tions,we give some general conditions to ensure the linear determinacy of the minimalspeed.Finally,we provide some more precise conditions that only rely on the parametersof the system such that the linear determinacy of the minimal speed is assured.展开更多
In this paper, a variational description of the minimal wave speed c(m, f) of wave fronts forthe reaction diffusion equations u_t=u_(xx)+u^mf(u) is given, where m>1 and f(u)~1-u.The continuity of c(m, f) in m and ...In this paper, a variational description of the minimal wave speed c(m, f) of wave fronts forthe reaction diffusion equations u_t=u_(xx)+u^mf(u) is given, where m>1 and f(u)~1-u.The continuity of c(m, f) in m and f is also proved. Especially, for f(u)=1-u, the estimateof the minimal wave speed c(m, f) is obtained.展开更多
This paper is devoted to investigating the selection mechanism of the minimal wave speed for traveling waves to an epidemic model.The determinacy of linear and nonlinear selections is further discussed by the upper-lo...This paper is devoted to investigating the selection mechanism of the minimal wave speed for traveling waves to an epidemic model.The determinacy of linear and nonlinear selections is further discussed by the upper-lower solutions and comparison principle.A threshold is defined by the eigenvalue problem of the linearized system.We show that the nonlinear determinacy is obtained as long as there exists a lower solution with a faster decay and a speed parameter that is larger than the threshold.When the speed parameter equals to the threshold,if there exists an upper solution satisfying proper limit behavior,then the linear selection is realized.For a special function of infection rate,we obtain a threshold parameter that determines the linear and nonlinear selections.展开更多
In this paper,we mainly investigate the dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria.We first establish the existence of spreading speed,and show that the spreading speed...In this paper,we mainly investigate the dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria.We first establish the existence of spreading speed,and show that the spreading speed coincides with the minimal wave speed of traveling wavefronts.Moreover,a lower bound estimate of the spreading speed is given.Then,we prove that the traveling wavefronts with large speeds are globally exponentially stable,when the initial perturbation around the traveling wavefronts decays exponentially asχ→-∞,but the initial perturbation can be arbitrarily large in other locations.The adopted methods are the weighted energy and the squeezing technique.展开更多
基金The second author is supported by NSF of China(11861056).
文摘In this paper,we study the linear determinacy of the minimal speed of traveling wave-fronts for a three-component competition system with nonlocal dispersal.We first trans-form this system into a cooperative system.Then,by constructing suitable upper solu-tions,we give some general conditions to ensure the linear determinacy of the minimalspeed.Finally,we provide some more precise conditions that only rely on the parametersof the system such that the linear determinacy of the minimal speed is assured.
基金This project is supported by the Doctoral Programme Foundation of Institution of Higher Education
文摘In this paper, a variational description of the minimal wave speed c(m, f) of wave fronts forthe reaction diffusion equations u_t=u_(xx)+u^mf(u) is given, where m>1 and f(u)~1-u.The continuity of c(m, f) in m and f is also proved. Especially, for f(u)=1-u, the estimateof the minimal wave speed c(m, f) is obtained.
基金supported by NSF of China (No.11971213)Natural Science Foundation of Gansu Province of China (No.21JR7RA535).
文摘This paper is devoted to investigating the selection mechanism of the minimal wave speed for traveling waves to an epidemic model.The determinacy of linear and nonlinear selections is further discussed by the upper-lower solutions and comparison principle.A threshold is defined by the eigenvalue problem of the linearized system.We show that the nonlinear determinacy is obtained as long as there exists a lower solution with a faster decay and a speed parameter that is larger than the threshold.When the speed parameter equals to the threshold,if there exists an upper solution satisfying proper limit behavior,then the linear selection is realized.For a special function of infection rate,we obtain a threshold parameter that determines the linear and nonlinear selections.
基金supported by NSF of China(11861056)NSF of Gansu Province(21JR7RA121)+1 种基金Department of Education of Gansu Province:Youth Doctoral Fund Project(2021QB-018)Northwest Normal University:Starting Fund for Doctoral Research(202103101204)。
文摘In this paper,we mainly investigate the dynamics of traveling wavefronts for a model describing host tissue degradation by bacteria.We first establish the existence of spreading speed,and show that the spreading speed coincides with the minimal wave speed of traveling wavefronts.Moreover,a lower bound estimate of the spreading speed is given.Then,we prove that the traveling wavefronts with large speeds are globally exponentially stable,when the initial perturbation around the traveling wavefronts decays exponentially asχ→-∞,but the initial perturbation can be arbitrarily large in other locations.The adopted methods are the weighted energy and the squeezing technique.