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

Qiwei Wu; Liping Luan

doi:10.3934/cpaa.2021003

Article Contents

2021, Volume 20, Issue 3: 995-1023. Doi: 10.3934/cpaa.2021003

This issue Previous Article Discrete diffusion semigroups associated with Jacobi-Dunkl and exceptional Jacobi polynomials Next Article An overdetermined problem associated to the Finsler Laplacian

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

Qiwei Wu^1, and
Liping Luan^2, ,

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

^* Corresponding author
^* Corresponding author

Received: July 31, 2020

Revised: October 31, 2020

Early access: January 2021

Published: March 2021

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q35, 35B40; Secondary: 35B65.

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References

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