On the interior boundary-value problem for the stationary Povzner equation with hard and soft interactions

Vladislav A. Panferov[1]

  • [1] Department of Mathematics and Statistics McMaster University Hamilton, Ontario L8S 4K1 Canada

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2004)

  • Volume: 3, Issue: 4, page 771-825
  • ISSN: 0391-173X

Abstract

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The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in L 1 is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angular cutoff. Boundary conditions of the diffuse reflection type, as well as the given incoming profile, are treated. The method is based on establishing the weak compactness of approximate solutions by using estimates of the entropy production.

How to cite

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Panferov, Vladislav A.. "On the interior boundary-value problem for the stationary Povzner equation with hard and soft interactions." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 3.4 (2004): 771-825. <http://eudml.org/doc/84549>.

@article{Panferov2004,
abstract = {The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in $L^1$ is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angular cutoff. Boundary conditions of the diffuse reflection type, as well as the given incoming profile, are treated. The method is based on establishing the weak compactness of approximate solutions by using estimates of the entropy production.},
affiliation = {Department of Mathematics and Statistics McMaster University Hamilton, Ontario L8S 4K1 Canada},
author = {Panferov, Vladislav A.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {771-825},
publisher = {Scuola Normale Superiore, Pisa},
title = {On the interior boundary-value problem for the stationary Povzner equation with hard and soft interactions},
url = {http://eudml.org/doc/84549},
volume = {3},
year = {2004},
}

TY - JOUR
AU - Panferov, Vladislav A.
TI - On the interior boundary-value problem for the stationary Povzner equation with hard and soft interactions
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2004
PB - Scuola Normale Superiore, Pisa
VL - 3
IS - 4
SP - 771
EP - 825
AB - The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in $L^1$ is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angular cutoff. Boundary conditions of the diffuse reflection type, as well as the given incoming profile, are treated. The method is based on establishing the weak compactness of approximate solutions by using estimates of the entropy production.
LA - eng
UR - http://eudml.org/doc/84549
ER -

References

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