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

Hailiang Li (School of Mathematical Sciences, Capital Normal University, Beijing, China)

Ming Mei (Department of Mathematics, Champlain College Saint-Lambert, Saint-Lambert, Quebec, Canada; and Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada)

Jianing Xu (School of Mathematical Sciences, Capital Normal University, Beijing, China)

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

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Received 6 November 2021

Accepted 7 May 2022

Published 27 December 2022