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oai:docta.ucm.es:20.500.14352/944602025-03-25T00:52:36Zcom_20.500.14352_14col_20.500.14352_15

Long time asymptotics for the semiconductor Vlasov-Poisson-Boltzmann equations Carpio Rodríguez, Ana María Cebrián, Elena Mustieles, F. J. In this paper we analyze the long time behavior of solutions to the one-dimensional Vlasov–Poisson–Boltzmann (VPB) equations for semiconductors in unbounded domains when only one type of carriers (electrons) are considered. We prove that the distribution of electrons tends for large times to a steady state of the VPB equations with vanishing collision term and the same total charge as the initial data. In the proof of the main result, the conservation law of charge, the balance of energy and entropy inequalities are rigorously derived. An important argument in the proof is to use a Lyapunov-type functional related to these physical quantities. 2024-01-22T15:35:01Z 2024-01-22T15:35:01Z 2001 journal article Carpio, A., et al. «LONG TIME ASYMPTOTICS FOR THE SEMICONDUCTOR VLASOV–POISSON–BOLTZMANN EQUATIONS». Mathematical Models and Methods in Applied Sciences, vol. 11, n.o 09, diciembre de 2001, pp. 1631-55. https://doi.org/10.1142/S0218202501001513. 0218-2025 https://hdl.handle.net/20.500.14352/94460 https://doi.org/10.1142/S0218202501001513 eng restricted access World Scientific Publishing