Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping
In this paper, we investigate the global existence and large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Possion equations with time and spacedependent damping in a bounded interval. Firstly, we prove the existence of entr...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/8881435 |
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| author | Yan Li Yanqiu Cheng Huimin Yu |
| author_facet | Yan Li Yanqiu Cheng Huimin Yu |
| author_sort | Yan Li |
| collection | DOAJ |
| description | In this paper, we investigate the global existence and large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Possion equations with time and spacedependent damping in a bounded interval. Firstly, we prove the existence of entropy solutions through vanishing viscosity method and compensated compactness framework. Based on the uniform estimates of density, we then prove the entropy solutions converge to the corresponding unique stationary solution exponentially with time. We generalize the existing results to the variable coefficient damping case. |
| format | Article |
| id | doaj-art-0bb449f50e5943b2a4e0368b58d7de5b |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-0bb449f50e5943b2a4e0368b58d7de5b2025-08-20T02:02:54ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/88814358881435Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient DampingYan Li0Yanqiu Cheng1Huimin Yu2Department of Mathematics, Shandong Normal University, Jinan 250014, ChinaDepartment of Mathematics, Shandong Normal University, Jinan 250014, ChinaDepartment of Mathematics, Shandong Normal University, Jinan 250014, ChinaIn this paper, we investigate the global existence and large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Possion equations with time and spacedependent damping in a bounded interval. Firstly, we prove the existence of entropy solutions through vanishing viscosity method and compensated compactness framework. Based on the uniform estimates of density, we then prove the entropy solutions converge to the corresponding unique stationary solution exponentially with time. We generalize the existing results to the variable coefficient damping case.http://dx.doi.org/10.1155/2020/8881435 |
| spellingShingle | Yan Li Yanqiu Cheng Huimin Yu Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping Advances in Mathematical Physics |
| title | Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping |
| title_full | Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping |
| title_fullStr | Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping |
| title_full_unstemmed | Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping |
| title_short | Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping |
| title_sort | existence and large time behavior of entropy solutions to one dimensional unipolar hydrodynamic model for semiconductor devices with variable coefficient damping |
| url | http://dx.doi.org/10.1155/2020/8881435 |
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