Abstract
Gajewski and Gröger used a convex thermodynamic potential, the free energy, in the analysis of the drift-diffusion model. We consider an energy model as an example of a system in which the temperature is a dynamic variable. In such systems the free energy is no convex functional. We introduce an approach to the transient problem for the model which is based on convex functionals which are related to the entropy and its conjugate potential and which allow the application of the tools of convex analysis. A semi-implicit method for the initial-boundary value problem arises on a rather natural way and basic estimates are proved for the solutions.
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Albinus, G. (1999). Remarks on the Convex Analysis of the Energy Model of Semiconductor Devices. In: Bungartz, HJ., Durst, F., Zenger, C. (eds) High Performance Scientific and Engineering Computing. Lecture Notes in Computational Science and Engineering, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60155-2_31
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DOI: https://doi.org/10.1007/978-3-642-60155-2_31
Publisher Name: Springer, Berlin, Heidelberg
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