EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 55 / No 4 (July-August 2021) ESAIM: M2AN, 55 4 (2021) 1323-1345 References
Open Access
Issue
ESAIM: M2AN
Volume 55, Number 4, July-August 2021
Page(s) 1323 - 1345
DOI https://doi.org/10.1051/m2an/2021022
Published online 07 July 2021
  1. C. Baranger, M. Bisi, S. Brull and L. Desvillettes, On the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic rarefied gases. Kinet. Relat. Models 11 (2018) 821–858. [Google Scholar]
  2. A. Bondesan, L. Boudin, M. Briant and B. Grec, Stability of the spectral gap for the Boltzmann multi-species operator linearized around non-equilibrium Maxwell distribution. Preprint arxiv:1811.08350 (2019). [Google Scholar]
  3. L. Boudin, B. Grec and V. Pavan, The Maxwell-Stefan diffusion limit for a kinetic model of mixtures with general cross sections. Nonlinear Anal. 159 (2017) 40–61. [Google Scholar]
  4. L. Boudin, B. Grec, M. Pavić and F. Salvarani, Diffusion asymptotics of a kinetic model for gaseous mixtures. Kinet. Relat. Models 6 (2013) 137–157. [CrossRef] [MathSciNet] [Google Scholar]
  5. L. Boudin and F. Salvarani, Compactness of linearized kinetic operators, in From particle systems to partial differential equations, III. In: Vol. 162 of Springer Proc. Math. Stat. Springer, Cham (2016) 73–97. [Google Scholar]
  6. M. Briant, Stability of global equilibrium for the multi-species Boltzmann equation in L∞ settings. Discrete Contin. Dyn. Syst. 36 (2016) 6669–6688. [Google Scholar]
  7. M. Briant, Perturbative theory for the Boltzmann equation in bounded domains with different boundary conditions. Kinet. Relat. Models 10 (2017) 329–371. [Google Scholar]
  8. M. Briant and E.S. Daus, The Boltzmann equation for a multi-species mixture close to global equilibrium. Arch. Ration. Mech. Anal. 222 (2016) 1367–1443. [Google Scholar]
  9. C. Cercignani, Rarefied gas dynamics: From basic concepts to actual calculations. Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge (2000) xviii+320. [Google Scholar]
  10. Z. Chen, L. Liu and L. Mu, DG-IMEX stochastic Galerkin schemes for linear transport equation with random inputs and diffusive scalings. J. Sci. Comput. 73 (2017) 566–592. [Google Scholar]
  11. E.S. Daus, S. Jin and L. Liu, Spectral convergence of the stochastic Galerkin approximation to the Boltzmann equation with multiple scales and large random perturbation in the collision kernel. Kinet. Relat. Models 12 (2019) 909–922. [Google Scholar]
  12. E.S. Daus, A. Jüngel, C. Mouhot and N. Zamponi, Hypocoercivity for a linearized multispecies Boltzmann system. SIAM J. Math. Anal. 48 (2016) 538–568. [Google Scholar]
  13. B. Després and B. Perthame, Uncertainty propagation; intrusive kinetic formulations of scalar conservation laws. SIAM/ASA J. Uncertain. Quantif. 4 (2016) 980–1013. [Google Scholar]
  14. L. Desvillettes, R. Monaco and F. Salvarani, A kinetic model allowing to obtain the energy law of polytropic gases in the presence of chemical reactions. Eur. J. Mech. B Fluids 24 (2005) 219–236. [Google Scholar]
  15. G. Dimarco, L. Pareschi and M. Zanella, Uncertainty quantification for kinetic models in socio-economic and life sciences, in Uncertainty quantification for hyperbolic and kinetic equations. In: Vol. 14 of SEMA SIMAI Springer Series. Springer, Cham (2017) 151–191. [Google Scholar]
  16. I.M. Gamba and M. Pavić-Čolić, On existence and uniqueness to homogeneous Boltzmann flows of monatomic gas mixtures. Arch. Ration. Mech. Anal. (2019). [Google Scholar]
  17. R.G. Ghanem and P.D. Spanos, Stochastic finite elements: A spectral approach. Springer-Verlag, New York (1991) x+214. [Google Scholar]
  18. V. Giovangigli, Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston Inc., Boston, MA (1999) xvi+321. [Google Scholar]
  19. M.P. Gualdani, S. Mischler and C. Mouhot, Factorization of non-symmetric operators and exponential H-theorem. Mém. Soc. Math. Fr. (NS) 153 (2017). [Google Scholar]
  20. M.D. Gunzburger, C.G. Webster and G. Zhang, Stochastic finite element methods for partial differential equations with random input data. Acta Numer. 23 (2014) 521–650. [CrossRef] [Google Scholar]
  21. J. Hu and S. Jin, Uncertainty quantification for kinetic equations, edited by S. Jin and L. Pareschi. In: SEMA-SIMAI Springer Series (2017) 193–229. [Google Scholar]
  22. S. Jin, J.-G. Liu and Z. Ma, Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro–macro decomposition-based asymptotic-preserving method. Res. Math. Sci. 4 (2017) 1–25. [Google Scholar]
  23. S. Jin and L. Liu, An asymptotic-preserving stochastic Galerkin method for the semiconductor Boltzmann equation with random inputs and diffusive scalings. Multiscale Model. Simul. 15 (2017) 157–183. [Google Scholar]
  24. S. Jin and L. Pareschi, eds., Uncertainty quantification for hyperbolic and kinetic equations. In: Vol. 14 of SEMA SIMAI Springer Series. Springer, Cham (2017). [CrossRef] [Google Scholar]
  25. Q. Li and L. Wang, Uniform regularity for linear kinetic equations with random input based on hypocoercivity. SIAM/ASA J. Uncertain. Quantif. 5 (2017) 1193–1219. [Google Scholar]
  26. L. Liu, A stochastic asymptotic-preserving scheme for the bipolar semiconductor Boltzmann-Poisson system with random inputs and diffusive scalings. J. Comput. Phys. 376 (2019) 634–659. [Google Scholar]
  27. L. Liu and S. Jin, Hypocoercivity based sensitivity analysis and spectral convergence of the stochastic Galerkin approximation to collisional kinetic equations with multiple scales and random inputs. Multiscale Model. Simul. 16 (2018) 1085–1114. [Google Scholar]
  28. L. Liu and M. Pirner, Hypocoercivity for a BGK model for gas mixtures. J. Differential Equations 267 (2019) 119–149. [Google Scholar]
  29. M. Loève, Probability Theory I. Springer-Verlag, New York (1977). [Google Scholar]
  30. C. Mouhot, Explicit coercivity estimates for the linearized Boltzmann and Landau operators. Commun. Partial Differ. Equ. 31 (2006) 1321–1348. [Google Scholar]
  31. R.C. Smith, Uncertainty quantification: Theory, implementation, and applications 12 (2014) XVIII+382. [Google Scholar]
  32. D. Xiu, Numerical methods for stochastic computations: A spectral method approach. Princeton University Press, Princeton, New Jersey (2010). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you