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# Communications in Mathematical Sciences

## Volume 21 (2023)

### Number 1

### Asymptotic behavior of solutions to the unipolar hydrodynamic model of semiconductors with time-dependent damping in bounded domain

Pages: 255 – 280

DOI: https://dx.doi.org/10.4310/CMS.2023.v21.n1.a12

#### Authors

#### Abstract

This paper concerns asymptotic behavior of solutions to the initial boundary-value problem for one-dimensional unipolar hydrodynamic model of semiconductors with time-dependent damping$-\frac{\rho u}{(1+t)^\lambda}$ for $\lambda \in (0,1)$. The damping effect is time-gradually-degenerate when $\lambda \in (0,1)$. We prove that the system admits a unique global smooth solution and the solution time-asymptotically converges to the constant steady-state in the sub-exponential form when the doping profile is completely flat. The adopted method of the proof is the elementary energy estimates but with some technical development.

#### Keywords

unipolar hydrodynamic model, semiconductor, time-dependent damping, initial boundary-value problem, convergence, steady-state

#### 2010 Mathematics Subject Classification

35B40, 35L50, 35L60, 35L65

Received 6 November 2021

Accepted 7 May 2022

Published 27 December 2022