# American Institute of Mathematical Sciences

March  2021, 20(3): 995-1023. doi: 10.3934/cpaa.2021003

## Large-time behavior of solutions to unipolar Euler-Poisson equations with time-dependent damping

 1 Department of Mathematics, Shanghai University, Shanghai 200444, China 2 Materials Genome Institute, Shanghai University, Shanghai 200444, China

* Corresponding author

Received  August 2020 Revised  November 2020 Published  January 2021

This paper is concerned with the Cauchy problem of the 1-D unipolar hydrodynamic model for semiconductor device, a system of Euler-Poisson equations with time-dependent damping effect $-J(1+t)^{-\lambda}$ for $-1<\lambda<1$, where $J$ denotes the current density, and the damping effect is asymptotically vanishing as $t \to \infty$ for $\lambda>0$, and asymptotically enhancing to infinity as $t \to \infty$ for $\lambda<0$. When the initial perturbation around the constant states are sufficiently small, by means of the time-weighted energy method, we prove that the smooth solutions to the Cauchy problem exist uniquely and globally. Particularly, we also obtain the large-time behavior of the solutions.

Citation: Qiwei Wu, Liping Luan. Large-time behavior of solutions to unipolar Euler-Poisson equations with time-dependent damping. Communications on Pure & Applied Analysis, 2021, 20 (3) : 995-1023. doi: 10.3934/cpaa.2021003
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