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Conservation laws and solutions of a quantum drift-diffusion model for semiconductors
Institution:1. Laboratory ”Group analysis of mathematical models in natural and engineering sciences”, Ufa State Aviation Technical University, 450 000 Ufa, Russia;2. Research Centre ALGA: Advances in Lie Group Analysis, Department of Mathematics and Natural Sciences, Blekinge Institute of Technology, SE-371 79 Karlskrona, Sweden;3. Department of Mathematics and Natural Sciences, Blekinge Institute of Technology, SE-371 79 Karlskrona, Sweden;1. A.N. Podgorny Institute for Mechanical Engineering Problems, National Academy of Sciences of Ukraine, 2/10 Dm. Pozharskoho St., 61046 Kharkiv, Ukraine;2. 377 H Administration Building, MC-348, 506 South Wright Street, Urbana, IL 61801, USA;1. University of Cagliari, DICAAR—Department of Civil and Environmental Engineering and Architecture, via Marengo, 2, I-09123 Cagliari, Italy;2. Intes GmbH, Schulze-Delitzsch-Straße 16, D-70565 Stuttgart, Germany;3. Technische Universität Dresden, Institut Statik und Dynamik der Tragwerke, Schumann-Straße 10, D-01062 Dresden, Germany;4. University of Sassari, DADU—Department of Architecture, Design and Urban Planning, Asilo Sella, via Garibaldi, 35, I-07041 Alghero (SS), Italy;1. Doctoral School in Theoretical and Applied Mechanics, Università di Roma La Sapienza, 18 Via Eudossiana, Rome;2. MeMoCS, International Research Center for the Mathematics & Mechanics of Complex Systems, Università dell׳Aquila, Italy;3. Department of Structural and Geotechnical Engineering, Università di Roma La Sapienza, 18 Via Eudossiana, Rome;4. Department of Physics, University Federico II, Naples, Via Cinthia I-80126, Naples, Italy
Abstract:A non-linear system of partial differential equations describing a quantum drift-diffusion model for semiconductor devices is investigated by methods of group analysis. An infinite number of conservation laws associated with symmetries of the model are found. These conservation laws are used for representing the system of equations under consideration in the conservation form. Exact solutions provided by the method of conservation laws are discussed. These solutions are different from invariant solutions.
Keywords:Quantum semiconductor  Drift-diffusion model  Non-linear self-adjointness  Conservation laws  Exact solutions
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