In this paper,the Cauchy problem of Boltzmann-Poisson system with the relaxation term is considered. The global existence and uniquessness of the smooth solution is proved under the small initial data.
This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the ...This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results on L1-theory under weaker conditons on initial boundary values.展开更多
In order to consider quantum transport under the influence of an electron-electron （e-e） interaction in a mesoscopic conductor,the Boltzmann equation and Poisson equation are investigated jointly.The analytical expr...In order to consider quantum transport under the influence of an electron-electron （e-e） interaction in a mesoscopic conductor,the Boltzmann equation and Poisson equation are investigated jointly.The analytical expressions of the distribution function for the Boltzmann equation and the self-consistent average potential concerned with e-e interaction are obtained,and the dielectric function appearing in the self-consistent average potential is naturally generalized beyond the Thomas-Fermi approximation.Then we apply these results to the tunneling junctions of a metal-insulator-semiconductor （MIS） in which the electrons are accumulated near the interface of the semiconductor,and we find that the e-e interaction plays an important role in the transport procedure of this system. The electronic density,electric current as well as screening Coulombic potential in this case are studied,and we reveal the time and position dependence of these physical quantities explicitly affected by the e-e interaction.展开更多
In this article, we are concerned with the construction of global smooth small-amplitude solutions to the Cauchy problem of the one species Vlasov-Poisson-Boltzmann system near Maxwellians for long-range interactions....In this article, we are concerned with the construction of global smooth small-amplitude solutions to the Cauchy problem of the one species Vlasov-Poisson-Boltzmann system near Maxwellians for long-range interactions. Compared with the former result obtained by Duan and Liu in [12] for the two species model, we do not ask the initial perturbation to satisfy the neutral condition and our result covers all physical collision kernels for the full range of intermolecular repulsive potentials.展开更多
In this paper we establish the convergence of the Vlasov-Poisson-Boltzmann system to the incompressible Euler equations in the so-called quasi-neutral regime. The convergence is rigorously proved for time intervals on...In this paper we establish the convergence of the Vlasov-Poisson-Boltzmann system to the incompressible Euler equations in the so-called quasi-neutral regime. The convergence is rigorously proved for time intervals on which the smooth solution of the Euler equations of the incompressible fluid exists. The proof relies on the relative-entropy method.展开更多
文摘In this paper,the Cauchy problem of Boltzmann-Poisson system with the relaxation term is considered. The global existence and uniquessness of the smooth solution is proved under the small initial data.
基金1. The NNSF (0111051400) of Henan Province2. The OYF (0016) of Henan Province.
文摘This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results on L1-theory under weaker conditons on initial boundary values.
基金Project supported by the National Natural Science Foundation of China (Grant No 10404037)
文摘In order to consider quantum transport under the influence of an electron-electron （e-e） interaction in a mesoscopic conductor,the Boltzmann equation and Poisson equation are investigated jointly.The analytical expressions of the distribution function for the Boltzmann equation and the self-consistent average potential concerned with e-e interaction are obtained,and the dielectric function appearing in the self-consistent average potential is naturally generalized beyond the Thomas-Fermi approximation.Then we apply these results to the tunneling junctions of a metal-insulator-semiconductor （MIS） in which the electrons are accumulated near the interface of the semiconductor,and we find that the e-e interaction plays an important role in the transport procedure of this system. The electronic density,electric current as well as screening Coulombic potential in this case are studied,and we reveal the time and position dependence of these physical quantities explicitly affected by the e-e interaction.
基金supported by the Fundamental Research Funds for the Central Universitiessupported by a grant from the National Science Foundation of China under contract 11501556+1 种基金supported by a grant from the National Natural Science Foundation under contract 11501187supported by three grants from the National Natural Science Foundation of China under contracts 10925103,11271160,and 11261160485
文摘In this article, we are concerned with the construction of global smooth small-amplitude solutions to the Cauchy problem of the one species Vlasov-Poisson-Boltzmann system near Maxwellians for long-range interactions. Compared with the former result obtained by Duan and Liu in [12] for the two species model, we do not ask the initial perturbation to satisfy the neutral condition and our result covers all physical collision kernels for the full range of intermolecular repulsive potentials.
基金the Special Funds of State Major Basic Research Projects(Grant 1999075107)The Grant of NSAF(No.10276036)+4 种基金NSFC(Grant 10431060)Tianyuan Youth Funds of China(Grant 10426030)NSFC(Grant 10501047)Nanjing University Talent Development FoundationNSFC(Grant 10471009)
文摘In this paper we establish the convergence of the Vlasov-Poisson-Boltzmann system to the incompressible Euler equations in the so-called quasi-neutral regime. The convergence is rigorously proved for time intervals on which the smooth solution of the Euler equations of the incompressible fluid exists. The proof relies on the relative-entropy method.
