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Rigorous validity of the Boltzmann equation for a thin layer of a rarefied gas
1. | Dipartimento di Matematica pura ed Applicata, Università dell’Aquila, Via Vetoio - Coppito, L’Aquila, 67100, Italy |
2. | Dipartimento di Matematica Guido Castelnuovo, Università La Sapienza, P.e Aldo Moro, 2, 67100 Roma, Italy |
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Yanpeng Jin, Ying Fu. Global Carleman estimate and its applications for a sixth-order equation related to thin solid films. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022072 |
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Rejeb Hadiji, Ken Shirakawa. Asymptotic analysis for micromagnetics of thin films governed by indefinite material coefficients. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1345-1361. doi: 10.3934/cpaa.2010.9.1345 |
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Xiao-Ping Wang, Ke Wang, Weinan E. Simulations of 3-D domain wall structures in thin films. Discrete and Continuous Dynamical Systems - B, 2006, 6 (2) : 373-389. doi: 10.3934/dcdsb.2006.6.373 |
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Yang Liu, Wenke Li. A class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4367-4381. doi: 10.3934/dcdss.2021112 |
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Tai-Ping Liu, Shih-Hsien Yu. Boltzmann equation, boundary effects. Discrete and Continuous Dynamical Systems, 2009, 24 (1) : 145-157. doi: 10.3934/dcds.2009.24.145 |
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Leif Arkeryd, Anne Nouri. On a Boltzmann equation for Haldane statistics. Kinetic and Related Models, 2019, 12 (2) : 323-346. doi: 10.3934/krm.2019014 |
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Marina Chugunova, Roman M. Taranets. New dissipated energy for the unstable thin film equation. Communications on Pure and Applied Analysis, 2011, 10 (2) : 613-624. doi: 10.3934/cpaa.2011.10.613 |
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Eric A. Carlen, Süleyman Ulusoy. Localization, smoothness, and convergence to equilibrium for a thin film equation. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4537-4553. doi: 10.3934/dcds.2014.34.4537 |
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Richard S. Laugesen. New dissipated energies for the thin fluid film equation. Communications on Pure and Applied Analysis, 2005, 4 (3) : 613-634. doi: 10.3934/cpaa.2005.4.613 |
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Changchun Liu, Jingxue Yin, Juan Zhou. Existence of weak solutions for a generalized thin film equation. Communications on Pure and Applied Analysis, 2007, 6 (2) : 465-480. doi: 10.3934/cpaa.2007.6.465 |
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Jian-Guo Liu, Jinhuan Wang. Global existence for a thin film equation with subcritical mass. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1461-1492. doi: 10.3934/dcdsb.2017070 |
[12] |
Claude Bardos, François Golse, Ivan Moyano. Linear Boltzmann equation and fractional diffusion. Kinetic and Related Models, 2018, 11 (4) : 1011-1036. doi: 10.3934/krm.2018039 |
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Yan Guo, Juhi Jang, Ning Jiang. Local Hilbert expansion for the Boltzmann equation. Kinetic and Related Models, 2009, 2 (1) : 205-214. doi: 10.3934/krm.2009.2.205 |
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Raffaele Esposito, Yan Guo, Rossana Marra. Validity of the Boltzmann equation with an external force. Kinetic and Related Models, 2011, 4 (2) : 499-515. doi: 10.3934/krm.2011.4.499 |
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El Miloud Zaoui, Marc Laforest. Stability and modeling error for the Boltzmann equation. Kinetic and Related Models, 2014, 7 (2) : 401-414. doi: 10.3934/krm.2014.7.401 |
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Alexander Bobylev, Åsa Windfäll. Boltzmann equation and hydrodynamics at the Burnett level. Kinetic and Related Models, 2012, 5 (2) : 237-260. doi: 10.3934/krm.2012.5.237 |
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Radjesvarane Alexandre. A review of Boltzmann equation with singular kernels. Kinetic and Related Models, 2009, 2 (4) : 551-646. doi: 10.3934/krm.2009.2.551 |
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Igor Kukavica, Mohammed Ziane. Regularity of the Navier-Stokes equation in a thin periodic domain with large data. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 67-86. doi: 10.3934/dcds.2006.16.67 |
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Huiqiang Jiang. Energy minimizers of a thin film equation with born repulsion force. Communications on Pure and Applied Analysis, 2011, 10 (2) : 803-815. doi: 10.3934/cpaa.2011.10.803 |
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Daniel Ginsberg, Gideon Simpson. Analytical and numerical results on the positivity of steady state solutions of a thin film equation. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1305-1321. doi: 10.3934/dcdsb.2013.18.1305 |
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