On the stationary Boltzmann equation

Leif Arkeryd[1]

  • [1] Department of Mathematics, Chalmers Institute of Technology, S-41296 Gothenburg, Sweden

Séminaire Équations aux dérivées partielles (2001-2002)

  • Volume: 2001-2002, page 1-11

Abstract

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For stationary kinetic equations, entropy dissipation can sometimes be used in existence proofs similarly to entropy in the time dependent situation. Recent results in this spirit obtained in collaboration with A. Nouri, are here presented for the nonlinear stationary Boltzmann equation in bounded domains of I R n with given indata and diffuse reflection on the boundary.

How to cite

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Arkeryd, Leif. "On the stationary Boltzmann equation." Séminaire Équations aux dérivées partielles 2001-2002 (2001-2002): 1-11. <http://eudml.org/doc/11039>.

@article{Arkeryd2001-2002,
abstract = {For stationary kinetic equations, entropy dissipation can sometimes be used in existence proofs similarly to entropy in the time dependent situation. Recent results in this spirit obtained in collaboration with A. Nouri, are here presented for the nonlinear stationary Boltzmann equation in bounded domains of $I\! \! R^\{n\}$ with given indata and diffuse reflection on the boundary.},
affiliation = {Department of Mathematics, Chalmers Institute of Technology, S-41296 Gothenburg, Sweden},
author = {Arkeryd, Leif},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-11},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {On the stationary Boltzmann equation},
url = {http://eudml.org/doc/11039},
volume = {2001-2002},
year = {2001-2002},
}

TY - JOUR
AU - Arkeryd, Leif
TI - On the stationary Boltzmann equation
JO - Séminaire Équations aux dérivées partielles
PY - 2001-2002
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2001-2002
SP - 1
EP - 11
AB - For stationary kinetic equations, entropy dissipation can sometimes be used in existence proofs similarly to entropy in the time dependent situation. Recent results in this spirit obtained in collaboration with A. Nouri, are here presented for the nonlinear stationary Boltzmann equation in bounded domains of $I\! \! R^{n}$ with given indata and diffuse reflection on the boundary.
LA - eng
UR - http://eudml.org/doc/11039
ER -

References

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  1. Arkeryd, L., Cercignani, C., ’On the convergence of solutions of the Enskog equation to solutions of the Boltzmann equation’, Comm. Part. Diff. Eqns. 14, 1989, 1071-1089. Zbl0688.76053
  2. A rkeryd, L., Nouri, A., ’The stationary Boltzmann equation in the slab with given weighted mass for hard and soft forces’, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 27, 1998, 533-556. Zbl0936.76076
  3. Arkeryd, L., Nouri, A., ’On the stationary Povzner equation in three space variables’, J. Math. Kyoto Univ. 39, 1999, 115-153. Zbl1010.35022
  4. Arkeryd, L., Nouri, A., ’ L 1 solutions to the stationary Boltzmann equation in a slab’, Ann. Fac. Sci. Toulouse Math. 9, 2000, 375-413. Zbl0991.45005
  5. Arkeryd, L., Nouri, A., ’The stationary Boltzmann equation in I R n with given indata’, to appear in Ann. Scuola Norm. Sup. di Pisa. Zbl1170.76350
  6. Cercignani, C., Illner, R., Pulvirenti, M., ’The mathematical theory of dilute gases’, Springer -Verlag, Berlin, 1994. Zbl0813.76001
  7. DiPerna, R. J., Lions, P. L., ’On the Cauchy problem for Boltzmann equations: Global existence and weak stability’, Ann. Math. 130, 1989, 321-366. Zbl0698.45010
  8. DiPerna, R. J., Lions, P. L., Meyer, Y., ’ L p regularity of velocity averages’, Anal. Non Lin. 8, 1991, 271-287. Zbl0763.35014
  9. Grad, H., ’High frequency sound recording according to Boltzmann equation’, SIAM J. Appl. Math. 14, 1966, 935-955. Zbl0163.23203
  10. Guiraud, J. P., ’Problème aux limites intérieur pour l’équation de Boltzmann en régime stationaire, faiblement non linéaire’, J. Méc. Théor. Appl. 11, 1972, 183-231. Zbl0245.76061
  11. Heintz, A., in preparation. 
  12. Maslova, N., ’Non linear evolution equations, Kinetic approach’, Series on Advances in Mathematics for Applied Sciences, Vol 10, World Scientific, 1993. Zbl0846.76002
  13. Panferov, V., ’On the existence of stationary solutions to the Povzner equation in a bounded domain’, 2000, submitted. 
  14. Ukai, S., Asano, K., ’Steady solutions of the Boltzmann equation for a gas flow past an obstacle; I existence’, Arch. Rat. Mech. Anal. 84, 1983, 249-291. Zbl0538.76070

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