Asymptotic Behavior of the Solution to a 3-D Simplified Energy-Transport Model for Semiconductors

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Volume 29, Issue 1

Chundi Liu, Yong Li & Shu Wang

DOI: 10.4208/jpde.v29.n1.7

J. Part. Diff. Eq., 29 (2016), pp. 71-88.

Published online: 2016-03

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Abstract

The well-posedness of smooth solution to a 3-Dsimplified Energy-Transport model is discussed in this paper. We prove the local existence, uniqueness, and asymptotic behavior of solution to the equations with hybrid cross-diffusion. The smooth solution convergences to a stationary solution with an exponential rate as time tends to infinity when the initial date is a small perturbation of the stationary solution.

Keywords

Energy-Transport model Gagliardo-Nirenberg inequality asymptotic behavior

AMS Subject Headings

42C40, 42C15

Email address

liu_chundi@emails.bjut.edu.cn (Chundi Liu)

yli@bjut.edu.cn (Yong Li)

wangshu@bjut.edu.cn (Shu Wang)

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@Article{JPDE-29-71, author = {Liu , ChundiLi , Yong and Wang , Shu}, title = {Asymptotic Behavior of the Solution to a 3-D Simplified Energy-Transport Model for Semiconductors}, journal = {Journal of Partial Differential Equations}, year = {2016}, volume = {29}, number = {1}, pages = {71--88}, abstract = { The well-posedness of smooth solution to a 3-Dsimplified Energy-Transport model is discussed in this paper. We prove the local existence, uniqueness, and asymptotic behavior of solution to the equations with hybrid cross-diffusion. The smooth solution convergences to a stationary solution with an exponential rate as time tends to infinity when the initial date is a small perturbation of the stationary solution.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v29.n1.7}, url = {http://global-sci.org/intro/article_detail/jpde/5080.html} }

TY - JOUR T1 - Asymptotic Behavior of the Solution to a 3-D Simplified Energy-Transport Model for Semiconductors AU - Liu , Chundi AU - Li , Yong AU - Wang , Shu JO - Journal of Partial Differential Equations VL - 1 SP - 71 EP - 88 PY - 2016 DA - 2016/03 SN - 29 DO - http://doi.org/10.4208/jpde.v29.n1.7 UR - https://global-sci.org/intro/article_detail/jpde/5080.html KW - Energy-Transport model KW - Gagliardo-Nirenberg inequality KW - asymptotic behavior AB - The well-posedness of smooth solution to a 3-Dsimplified Energy-Transport model is discussed in this paper. We prove the local existence, uniqueness, and asymptotic behavior of solution to the equations with hybrid cross-diffusion. The smooth solution convergences to a stationary solution with an exponential rate as time tends to infinity when the initial date is a small perturbation of the stationary solution.

Liu , ChundiLi , Yong and Wang , Shu. (2016). Asymptotic Behavior of the Solution to a 3-D Simplified Energy-Transport Model for Semiconductors. Journal of Partial Differential Equations. 29 (1). 71-88. doi:10.4208/jpde.v29.n1.7

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