Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping

Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping

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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 Canine - Treats - Cakes 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 LAVENDER exponentially with time.We generalize the existing results to the variable coefficient damping case.