5,447 research outputs found
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
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
Global exponential stability of classical solutions to the hydrodynamic model for semiconductors
In this paper, the global well-posedness and stability of classical solutions
to the multidimensional hydrodynamic model for semiconductors on the framework
of Besov space are considered. We weaken the regularity requirement of the
initial data, and improve some known results in Sobolev space. The local
existence of classical solutions to the Cauchy problem is obtained by the
regularized means and compactness argument. Using the high- and low- frequency
decomposition method, we prove the global exponential stability of classical
solutions (close to equilibrium). Furthermore, it is also shown that the
vorticity decays to zero exponentially in the 2D and 3D space. The main
analytic tools are the Littlewood-Paley decomposition and Bony's para-product
formula.Comment: 18 page
Existence analysis for a simplified transient energy-transport model for semiconductors
A simplified transient energy-transport system for semiconductors subject to
mixed Dirichlet-Neumann boundary conditions is analyzed. The model is formally
derived from the non-isothermal hydrodynamic equations in a particular
vanishing momentum relaxation limit. It consists of a drift-diffusion-type
equation for the electron density, involving temperature gradients, a nonlinear
heat equation for the electron temperature, and the Poisson equation for the
electric potential. The global-in-time existence of bounded weak solutions is
proved. The proof is based on the Stampacchia truncation method and a careful
use of the temperature equation. Under some regularity assumptions on the
gradients of the variables, the uniqueness of solutions is shown. Finally,
numerical simulations for a ballistic diode in one space dimension illustrate
the behavior of the solutions
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