Exponential equilibration of an electro-energy-reaction-diffusion system arising from a two-level semiconductor model
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909727691112448 |
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| author | Kniely, Michael |
| author_facet | Kniely, Michael |
| contents | We consider a thermodynamically correct framework for electro-energy-reaction-diffusion systems, which feature a monotone entropy functional while conserving the total charge and the total energy. For these systems, we construct a relative entropy functional, which acts as a Lyapunov functional, and we also give an expression for the related entropy production functional. The main result of this note is the constructive derivation of an explicit entropy-entropy production inequality in a special situation, namely for a two-level semiconductor model of Shockley-Read-Hall type. Supposing that global bounded solutions exist, we show that the relative entropy decays exponentially along trajectories of the underlying system. As a consequence, these global solutions converge to the equilibrium at an exponential rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential equilibration of an electro-energy-reaction-diffusion system arising from a two-level semiconductor model Kniely, Michael Analysis of PDEs 35Q79 (Primary) 78A30, 35B40, 35K57, 35Q81 (Secondary) We consider a thermodynamically correct framework for electro-energy-reaction-diffusion systems, which feature a monotone entropy functional while conserving the total charge and the total energy. For these systems, we construct a relative entropy functional, which acts as a Lyapunov functional, and we also give an expression for the related entropy production functional. The main result of this note is the constructive derivation of an explicit entropy-entropy production inequality in a special situation, namely for a two-level semiconductor model of Shockley-Read-Hall type. Supposing that global bounded solutions exist, we show that the relative entropy decays exponentially along trajectories of the underlying system. As a consequence, these global solutions converge to the equilibrium at an exponential rate. |
| title | Exponential equilibration of an electro-energy-reaction-diffusion system arising from a two-level semiconductor model |
| topic | Analysis of PDEs 35Q79 (Primary) 78A30, 35B40, 35K57, 35Q81 (Secondary) |
| url | https://arxiv.org/abs/2504.03534 |