On the entropy method and exponential convergence to equilibrium for a recombination–drift–diffusion system with self-consistent potential
We consider a Shockley–Read–Hall recombination–drift–diffusion model coupled to Poisson’s equation and subject to boundary conditions, which imply conservation of the total charge. As main result, we derive an explicit functional inequality between relative entropy and entropy production rate, which...
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| Published in | Applied mathematics letters Vol. 79; pp. 196 - 204 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.05.2018
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| Online Access | Get full text |
| ISSN | 0893-9659 1873-5452 |
| DOI | 10.1016/j.aml.2017.12.017 |
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| Abstract | We consider a Shockley–Read–Hall recombination–drift–diffusion model coupled to Poisson’s equation and subject to boundary conditions, which imply conservation of the total charge. As main result, we derive an explicit functional inequality between relative entropy and entropy production rate, which implies exponential convergence to equilibrium with explicit constant and rate. We report that the key entropy–entropy production inequality ought rather not to be formulated on the states space of the parabolic–elliptic system, but on the reduced states space of the associated nonlocal drift–diffusion problem, where the Poisson equation is replaced by the corresponding Green function. |
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| AbstractList | We consider a Shockley–Read–Hall recombination–drift–diffusion model coupled to Poisson’s equation and subject to boundary conditions, which imply conservation of the total charge. As main result, we derive an explicit functional inequality between relative entropy and entropy production rate, which implies exponential convergence to equilibrium with explicit constant and rate. We report that the key entropy–entropy production inequality ought rather not to be formulated on the states space of the parabolic–elliptic system, but on the reduced states space of the associated nonlocal drift–diffusion problem, where the Poisson equation is replaced by the corresponding Green function. |
| Author | Kniely, Michael Fellner, Klemens |
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| Cites_doi | 10.1002/zamm.19960760502 10.1016/j.jmaa.2005.07.003 10.3934/krm.2010.3.427 10.1016/j.na.2017.02.007 10.1080/00036819608840428 10.1142/S0218202508002735 10.1002/zamm.19970771105 10.1137/16M1073935 10.1007/s10884-014-9394-x 10.1002/mana.19831120103 10.1142/S0218202595000292 10.4171/RMI/541 |
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| Keywords | Self-consistent potential Shockley–Read–Hall recombination Convergence to equilibrium Semiconductor model Drift-diffusion systems Entropy method |
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| Snippet | We consider a Shockley–Read–Hall recombination–drift–diffusion model coupled to Poisson’s equation and subject to boundary conditions, which imply conservation... |
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| SubjectTerms | Convergence to equilibrium Drift-diffusion systems Entropy method Self-consistent potential Semiconductor model Shockley–Read–Hall recombination |
| Title | On the entropy method and exponential convergence to equilibrium for a recombination–drift–diffusion system with self-consistent potential |
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