In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries （KdV for short） equation. By estimating the resolvent of the corresponding linear operator...In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries （KdV for short） equation. By estimating the resolvent of the corresponding linear operator, the authors conclude that the semigroup 3 generated by the linear operator is not analytic but of Gevrey class δ ε （5, ） for t 〉 0,展开更多
Considering the immune response and intracellular delay, we propose a two-strain virus model and investigate dynamics of this mathematical model. The global dynamics of the model are completely determined by introduci...Considering the immune response and intracellular delay, we propose a two-strain virus model and investigate dynamics of this mathematical model. The global dynamics of the model are completely determined by introducing suitable Lyapunov functionals. We show that if the basic reproduction number is less than one, then both strains die out; but when the number is greater than one, at least one of the strains become endemic depending on the parameter values. The theoretical results provide some useful information on the dynamics of the two strains virus.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11401021,11471044,11771336,11571257)the LIASFMA,the ANR project Finite4SoS(No.ANR 15-CE23-0007)the Doctoral Program of Higher Education of China(Nos.20130006120011,20130072120008)
文摘In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries （KdV for short） equation. By estimating the resolvent of the corresponding linear operator, the authors conclude that the semigroup 3 generated by the linear operator is not analytic but of Gevrey class δ ε （5, ） for t 〉 0,
基金supported by Scientific Research Fund of Hunan Provincial Education Department(13K012)National Natural Science Foundation of China(61102035)
文摘Considering the immune response and intracellular delay, we propose a two-strain virus model and investigate dynamics of this mathematical model. The global dynamics of the model are completely determined by introducing suitable Lyapunov functionals. We show that if the basic reproduction number is less than one, then both strains die out; but when the number is greater than one, at least one of the strains become endemic depending on the parameter values. The theoretical results provide some useful information on the dynamics of the two strains virus.
