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Large time behavior of solutions to a bipolar hydrodynamic model with big data and vacuum
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In this article, a physically relevant hydrodynamic model for the bipolar semiconductor device with insulating boundary conditions and a non-flat doping profile is considered and the corresponding steady solutions are unique and satisfy some bounded estimates, which are essential in the following consideration.Abstract:
In this note, we consider a physically relevant hydrodynamic model for the bipolar semiconductor device with insulating boundary conditions and a non-flat doping profile. We prove that the corresponding steady solutions are unique and satisfy some bounded estimates, which are essential in the following consideration. For the hydrodynamic model, by means of a technical energy method and a proper entropy dissipation estimate, the large time behavior framework for any uniformly bounded weak entropy solutions with vacuum is presented. The solutions are shown to converge to the stationary solutions in L 2 norm and an exponential decay rate is also derived. No smallness and regularity conditions are assumed and the doping profile is permitted to be of big variation.read more
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Oscillation of damped second order quasilinear wave equations with mixed arguments
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References
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Journal ArticleDOI
Divergence‐Measure Fields and Hyperbolic Conservation Laws
Gui-Qiang Chen,Hermano Frid +1 more
TL;DR: In this paper, a class of L 1 vector fields, called divergence-measure vector fields (DMEFs), are analyzed and the Gauss-Green formula, the normal traces over subsets of Lipschitz boundaries, and the product rule for this class of vector fields are established.
Journal ArticleDOI
On a one-dimensional steady-state hydrodynamic model for semiconductors
Pierre Degond,Peter A. Markowich +1 more
TL;DR: In this paper, a hydrodynamic model for semiconductors is presented, where the energy equation is replaced by a pressure-density relationship, and the authors prove existence of smooth solutions and a uniqueness result in the subsonic case, characterized by a smallness assumption on the current flowing through the device.
Journal ArticleDOI
Large time behavior of the solutions to a hydrodynamic model for semiconductors
TL;DR: The global existence of smooth solutions to the Cauchy problem for the one-dimensional isentropic Euler--Poisson model for semiconductors for small initial data is established and it is shown that, as $t\to\infty$, these solutions converge to the stationary solutions of the drift-diffusion equations.
Journal ArticleDOI
The bipolar hydrodynamic model for semiconductors and the drift-diffusion equations
TL;DR: In this article, the authors established the existence of entropy solutions for a bipolar hydrodynamic model for semiconductors and showed that the limit of an appropriate (scaled) sequence of entropy solution is a solution of the classical drift-diffusion equations.
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