Publications

• N. Bernhoff, Laurent Boudin, Milana Cotic, Berenice Grec, Compactness of linearized Boltzmann operators for polyatomic gases, in Mathematical models for interacting dynamics on networks (mat-dyn-net), accepted, 2024, 25pp.,  arXiv: 2407.11452

• N. Bernhoff, Discrete Boltzmann equation for anyons, in Mathematical models for interacting dynamics on networks (mat-dyn-net), accepted, 2024, 15pp.

• N. Bernhoff, Linearized Boltzmann Collision Operator for a Mixture of Monatomic and Polyatomic Chemically Reacting Species, J. Math. Chem., 62, 2024, 1935-1964

• N. Bernhoff, Compactness Property of the Linearized Boltzmann Collision Operator for a Mixture of Monatomic and Polyatomic Species, J. Stat. Phys., 191, 2024, 32:1-35

• N. Bernhoff, Compactness Property of the Linearized Boltzmann Collision Operator for a Multicomponent Polyatomic Gas, J. Math. Anal. Appl., 537, 2024, 128265:1-31

• N. Bernhoff, Linear Half-Space Problems in Kinetic Theory: Abstract Formulation and Regime Transitions, Int. J. Math., 34, 2023, 2350091:1-41 (arXiv: 2201.03459)

• N. Bernhoff, Discrete Quantum Kinetic Equation, La Mat., 2, 2023, 836-860

• N. Bernhoff, Linearized Boltzmann Collision Operator: II. Polyatomic Molecules Modeled by a Continuous Internal Energy Variable, Kinet. Relat. Models, 16, 2023, 828-849 (arXiv: 2201.01377)

• N. Bernhoff, Half-Space Problems for the Boltzmann Equation of Multicomponent Mixtures, in From Kinetic Theory to Turbulence Modeling, P. Barbante, F.D. Belgiorno, S. Lorenzani, and L. Valdettaro, eds., Springer, 2023, pp. 45-57

• N. Bernhoff, Linearized Boltzmann Collision Operator: I. Polyatomic Molecules Modeled by a Discrete Internal Energy Variable and Multicomponent Mixtures, Acta Appl. Math. 183, 2023, 3:1-45

• N. Bernhoff and F. Golse, On the Boundary Layer Equations with Phase Transition in the Kinetic Theory of Gases, Arch. Ration. Mech. Anal., 240, 2021, 51-98 Publishers correction Arch. Ration. Mech. Anal., 241, 2021, 137

The following article appeared in AIP Conference Proceedings 2132 and may be found at
https://doi.org/10.1063/1.5119631

• N. Bernhoff, Discrete Quantum Boltzmann Equation, AIP Conf. Proc., 2132, 2019, pp.130011-1-9
  This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing

• N. Bernhoff, Discrete Velocity Models for Polyatomic Molecules without Nonphysical Collision Invariants, J. Stat. Phys., 172, 2018, 742-761

• N. Bernhoff, Boundary Layers for Discrete Kinetic Models: Multicomponent Mixtures, Polyatomic Molecules, Bimolecular Chemical Reactions, and Quantum Kinetic Equations, Kinet. Relat. Models, 10, 2017, 925-955
  This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Kinetic and Related Models following peer review. The definitive publisher-authenticated version is available online at: https://www.aimsciences.org/article/doi/10.3934/krm.2017037

The following article appeared in AIP Conference Proceedings 1786 and may be found at
http://dx.doi.org/10.1063/1.4967543

• N. Bernhoff, Discrete Velocity Models for Multicomponent Mixtures and Polyatomic Molecules without Nonphysical Collision Invariants and Shock Profiles, AIP Conf. Proc., 1786, 2016, 040005-1-8
  This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing

• N. Bernhoff and M. Vinerean, Discrete Velocity Models for Mixtures without Nonphysical Collision Invariants, J. Stat. Phys., 165, 2016, 434-453

• N. Bernhoff, Boundary Layers and Shock Profiles for the Broadwell Model, Int. J. Differ. Equ., 2016, 2016, 5801728:1-8

• N. Bernhoff, Half-Space Problems for a Linearized Discrete Quantum Kinetic Equation, J. Stat. Phys., 159, 2015, 358-379
  The final publication is available at www.springerlink.com Journal link

The following article appeared in AIP Conference Proceedings 1501 and may be found at
http://dx.doi.org/10.1063/1.4769509

• N. Bernhoff, Boundary Layers for the Nonlinear Discrete Boltzmann Equation: Condensing Vapor Flow in the Presence of a Non-Condensable Gas, AIP Conf. Proc., 1501, 2012, 223-230
  This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing

• N. Bernhoff, Half-Space Problem for the Discrete Boltzmann Equation: Condensing Vapor Flow in the Presence of a Non-Condensable Gas, J. Stat. Phys., 147, 2012, 1156-1181
  The final publication is available at www.springerlink.com Journal link

• N. Bernhoff, Boundary Layers and Shock Profiles for the Discrete Boltzmann Equation for Mixtures, Kinet. Relat. Models, 5, 2012, 1-19
  This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Kinetic and Related Models following peer review. The definitive publisher-authenticated version is available online at: https://www.aimsciences.org/article/doi/10.3934/krm.2012.5.1

• N. Bernhoff, On Half-Space Problems for the Weakly Non-Linear Discrete Boltzmann Equation, Kinet. Relat. Models, 3, 2010, 195-222
  This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Kinetic and Related Models following peer review. The definitive publisher-authenticated version is available online at: https://www.aimsciences.org/article/doi/10.3934/krm.2010.3.195

• N. Bernhoff, On Half-Space Problems for the Discrete Boltzmann Equation, Nuovo Cim., 33 C, 2010, 47-54
  The original publication is available at http://www.sif.it/SIF/en/portal/journals Journal link

• N. Bernhoff, On Half-Space Problems for the Linearized Discrete Boltzmann Equation, Riv. Mat. Univ. Parma, 9, 2008, 73-124 Journal link

• N. Bernhoff and A.V. Bobylev, Weak Shock Waves for the General Discrete Velocity Model of the Boltzmann Equation, Commun. Math. Sci., 5, 2007, 815-832 Journal link

• N. Bernhoff and A.V. Bobylev, Weak Shock Wave Solutions for the Discrete Boltzmann Equation, Rarefied Gas Dynamics: Proceeedings of the 25th International Symposium on Rarefied Gas Dynamics, Saint-Petersburg, Russia, July 21-28, 2006, M.S. Ivanov and A.K. Rebrov, eds., Publishing House of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 2007, pp.173-178

• A.V. Bobylev and N. Bernhoff, Discrete Velocity Models and Dynamical Systems, in Lecture Notes on the Discretization of the Boltzmann Equation, N. Bellomo and R. Gatignol, eds., World Scientific Publishing Co, 2003, pp.203-222 Preview (Google Book Search)