In this paper, we investigate a one-dimensional bipolar quantum drift-diffusion model from semiconductor devices. We mainly show the long-time behavior of solutions to the one-dimensional bipolar quantum drift-diffusi...In this paper, we investigate a one-dimensional bipolar quantum drift-diffusion model from semiconductor devices. We mainly show the long-time behavior of solutions to the one-dimensional bipolar quantum drift-diffusion model in a bounded domain. That is, we prove the existence of the global attractor for the solution.展开更多
First, we show that the theorem by Hirsch which guarantees the existence of carrying simplex for competitive system on any n-rectangle： {x ∈ R^n ： 0 ≤ xi ≤ ki, i = 1,..., n} still holds. Next, based on the theore...First, we show that the theorem by Hirsch which guarantees the existence of carrying simplex for competitive system on any n-rectangle： {x ∈ R^n ： 0 ≤ xi ≤ ki, i = 1,..., n} still holds. Next, based on the theorem a competitive system with the linear structure saturation defined on the n-rectangle is investigated, which admits a unique （n - 1）- dimensional carrying simplex as a global attractor. Further, we focus on the whole dynamical behavior of the three-dimensional case, which has a unique locally asymptotically stable positive equilibrium. Hopf bifurcations do not occur. We prove that any limit set is either this positive equilibrium or a limit cycle. If limit cycles exist, the number of them is finite. We also give a criterion for the positive equilibrium to be globally asymptotically stable.展开更多
基金Supported by the National Natural Science Foundation of China(11671134)
文摘In this paper, we investigate a one-dimensional bipolar quantum drift-diffusion model from semiconductor devices. We mainly show the long-time behavior of solutions to the one-dimensional bipolar quantum drift-diffusion model in a bounded domain. That is, we prove the existence of the global attractor for the solution.
文摘First, we show that the theorem by Hirsch which guarantees the existence of carrying simplex for competitive system on any n-rectangle： {x ∈ R^n ： 0 ≤ xi ≤ ki, i = 1,..., n} still holds. Next, based on the theorem a competitive system with the linear structure saturation defined on the n-rectangle is investigated, which admits a unique （n - 1）- dimensional carrying simplex as a global attractor. Further, we focus on the whole dynamical behavior of the three-dimensional case, which has a unique locally asymptotically stable positive equilibrium. Hopf bifurcations do not occur. We prove that any limit set is either this positive equilibrium or a limit cycle. If limit cycles exist, the number of them is finite. We also give a criterion for the positive equilibrium to be globally asymptotically stable.
