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Group analysis of kinetic equations in a non-linear thermal transport problem
Affiliation:1. Laboratory GAMMNES, Ufa State Aviation Technical University, Ufa, Russia;2. Research Center ALGA, Blekinge Institute of Technology, Karlskrona, Sweden;3. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia;4. Center for Fundamental and Applied Research, VNIIA, ROSATOM, Moscow, Russia;5. School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand;6. P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia;1. Department of Mathematics, University of Utah, 155 S. 1400 E. Salt Lake City, UT 84112, USA;2. Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany;3. University of Bonn, Steinmann Institute, Department of Geophysics, Meckenheimer Allee 176, D-53115 Bonn, Germany;1. IMAG, Université de Montpellier, CC051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France;2. Equipe BIOSP, INRA Avignon, Domaine Saint Paul, Site Agroparc, 84914 Avignon Cedex 9, France;1. Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia;2. Mathematics Department, University of Education, Lahore, Pakistan;3. Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. Department of Mathematics, Università di Ferrara, Via Machiavelli, 35, I-44121 Ferrara, Italy;2. Department of Mathematics & Research Center of Applied Mathematics, University of Bologna, Via Saragozza 8, 40123 Bologna, Italy
Abstract:An application of modern group analysis to electron kinetic equations in non-linear thermal transport problem is discussed. The admitted symmetry group is calculated, and the optimal system of one and two-dimensional subalgebras is constructed. Representations of invariant solutions are presented.
Keywords:Symmetry  Invariant solution  Kinetic equations  Thermal transport problem
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