700 research outputs found

    Semiclassical and relaxation limits of bipolar quantum hydrodynamic model

    Get PDF
    The global in-time semiclassical and relaxation limits of the bipolar quantum hydrodynamic model for semiconductors are investigated in R3R^3. We prove that the unique strong solution converges globally in time to the strong solution of classical bipolar hydrodynamical equation in the process of semiclassical limit and to that of the classical Drift-Diffusion system under the combined relaxation and semiclassical limits.Comment: 21 page

    Critical Thresholds in 2D Restricted Euler-Poisson Equations

    Get PDF
    We provide a complete description of the critical threshold phenomena for the two-dimensional localized Euler-Poisson equations, introduced by the authors in [Liu & Tadmor, Comm. Math Phys., To appear]. Here, the questions of global regularity vs. finite-time breakdown for the 2D Restricted Euler-Poisson solutions are classified in terms of precise explicit formulae, describing a remarkable variety of critical threshold surfaces of initial configurations. In particular, it is shown that the 2D critical thresholds depend on the relative size of three quantities: the initial density, the initial divergence as well as the initial spectral gap, that is, the difference between the two eigenvalues of the 2×22 \times 2 initial velocity gradient

    Algebraic time-decay for the bipolar quantum hydrodynamic model

    Full text link
    The initial value problem is considered in the present paper for bipolar quantum hydrodynamic model for semiconductors (QHD) in R3\mathbb{R}^3. We prove that the unique strong solution exists globally in time and tends to the asymptotical state with an algebraic rate as t+t\to+\infty. And, we show that the global solution of linearized bipolar QHD system decays in time at an algebraic decay rate from both above and below. This means in general, we can not get exponential time-decay rate for bipolar QHD system, which is different from the case of unipolar QHD model (where global solutions tend to the equilibrium state at an exponential time-decay rate) and is mainly caused by the nonlinear coupling and cancelation between two carriers. Moreover, it is also shown that the nonlinear dispersion does not affect the long time asymptotic behavior, which by product gives rise to the algebraic time-decay rate of the solution of the bipolar hydrodynamical model in the semiclassical limit.Comment: 23 page
    corecore