700 research outputs found
Semiclassical and relaxation limits of bipolar quantum hydrodynamic model
The global in-time semiclassical and relaxation limits of the bipolar quantum
hydrodynamic model for semiconductors are investigated in . 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
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 initial velocity gradient
Algebraic time-decay for the bipolar quantum hydrodynamic model
The initial value problem is considered in the present paper for bipolar
quantum hydrodynamic model for semiconductors (QHD) in . We prove
that the unique strong solution exists globally in time and tends to the
asymptotical state with an algebraic rate as . 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
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