Abstract
In this paper, we investigate the global existence and large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Possion equations with time and spacedependent damping in a bounded interval. Firstly, we prove the existence of entropy solutions through vanishing viscosity method and compensated compactness framework. Based on the uniform estimates of density, we then prove the entropy solutions converge to the corresponding unique stationary solution exponentially with time. We generalize the existing results to the variable coefficient damping case.
Highlights
The present paper is concerned with the one-dimensional isentropic Euler-Possion model for semiconductor devices with damping:
For 1 < γ ≤ 3 and variable coefficient damping, we shall first verify the assumption in [11], where the density is assumed to be uniformly bounded with respect to space x and time t and use the entropy inequality to consider the large time behavior of the obtained solutions
Our main results in this paper are as follows
Summary
The present paper is concerned with the one-dimensional isentropic Euler-Possion model for semiconductor devices with damping:. For 1 < γ ≤ 3 and variable coefficient damping, we shall first verify the assumption in [11], where the density is assumed to be uniformly bounded with respect to space x and time t and use the entropy inequality to consider the large time behavior of the obtained solutions. Based on the related results in [12,13,14,15,16], we are convinced that the method developed in this paper can be used to bipolar Euler-Poisson system with time depended damping. There exists a global entropy solution ðρ, m, EÞðx, tÞ of the initial-boundary value problems (1) and (3) satisfying.
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