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AbstractAbstract
[en] We prove the stability and existence of global solutions of Boltzmann equations under general assumptions on the collision operators and the initial conditions. In particular, we introduce a new formulation of the equation and we observe some weak continuity properties of the collision operator
[fr]
Nous demontrons la stabilite et l'existence de solutions globales de l'equation de Boltzmann sous des hypotheses generales portant sur l'operateur de collision et les donnees initiales. Nous introduisons notamment une nouvelle formulation de l'equation et mettons en lumiere des mecanismes de continuite faible de l'operateur de collisionOriginal Title
Solutions globales de l'equation de Boltzmann
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Journal Article
Journal
Comptes Rendus de l'Academie des Sciences. Serie 1; ISSN 0764-4442;
; CODEN CASME; v. 306(7); p. 343-346

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AbstractAbstract
[en] For the simplest of the discrete models of the Boltzmann equation: the Broadwell model, exact solutions have been obtained by Cornille in the form of bisolitons. In the present Note, we build exact solutions for more complex models
[fr]
Pour le plus simple des modeles discrets de l'equation de Boltzmann: le modele de Broadwell, des solutions exactes ont ete obtenues par Cornille, sous forme de bisolitons. Dans la presente Note, nous construisons des solutions exactes pour des modeles plus complexesOriginal Title
Solutions exactes pour certains modeles discrets de l'equation de Boltzmann
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Journal Article
Journal
Comptes Rendus des Seances de l'Academie des Sciences. Serie 1; CODEN CHASA; v. 304(1); p. 29-34
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Wood, A.M.
Glasgow Univ. (United Kingdom)1999
Glasgow Univ. (United Kingdom)1999
AbstractAbstract
No abstract available
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Source
Sep 1999; [vp.]; Available from British Library Document Supply Centre- DSC:DXN033933; Thesis (Ph.D.)
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Miscellaneous
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Thesis/Dissertation
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Cornille, H.
CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique1988
CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique1988
AbstractAbstract
[en] We have constructed 2+1 dimensional exact solutions (space x, y time t) for three models: i) the square velocity model and the cubic model (with eight velocities oriented towards the eight corners) which satisfy the same type of nonlinear equations, ii) the Broadwell model. The main difficulty is the positivity condition Ni>0 for the densities Ni. We have obtained three classes of exact solutions: i) densities relaxing towards noniform Maxwellians ii) shock wave iii) semi-periodic solutions
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Source
1988; 3 p; 16. International Symposium on rarefied gas dynamics; Pasadena, CA (USA); 10-16 Jul 1988
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Report
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AbstractAbstract
[en] A new and relativistic formulation of Boltzmann's equation is presented
[fr]
On presente une formulation nouvelle et relativiste de l'equation de BoltzmannOriginal Title
Sur une nouvelle formulation de l'equation de Boltzmann
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Source
Centre National de la Recherche Scientifique, 75 - Paris (France); Colloques internationaux du Centre National de la Recherche Scientifique; no. 220; p. 309-312; 1974; Centre National de la Recherche Scientifique; Paris, France; International colloquium on gravitational waves and radiations; Paris, France; 18 Jun 1973
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Book
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AbstractAbstract
[en] We construct a model of discrete Boltzmann distribution with 2n velocities. In certain cases, the exact solutions we can calculate enable us to resolve the Cauchy's problem and obtain global solutions
[fr]
Nous construisons un modele de distribution discrete de Boltzmann a 2n vitesses. Dans certains cas les solutions exactes qu'on peut calculer permettent de resoudre le probleme de Cauchy et d'obtenir des solutions globalesOriginal Title
Sur une classe de solutions exactes des equations de Boltzmann en theorie discrete
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Journal Article
Journal
Comptes Rendus de l'Academie des Sciences, Serie 1; ISSN 0764-4442;
; CODEN CASME; v. 310(7); p. 603-606

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AbstractAbstract
No abstract available
Original Title
Die Entwicklung des Streukernes der nichtlinearen Boltzmanngleichung nach den natuerlichen Stoss- und Streuwinkeln im Laborsystem
Primary Subject
Source
Oesterreichische Physikalische Gesellschaft, Vienna; 109 p; 1986; p. 58; Austrian Physical Society - Annual convention 1986; Innsbruck (Austria); 22-26 Sep 1986; Published in summary form only.
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Miscellaneous
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Cornille, H.
CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Inst. de Recherche Fondamentale (IRF)1985
CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Inst. de Recherche Fondamentale (IRF)1985
AbstractAbstract
[en] We review recent results obtained for inhomogeneous distributions, solutions of d > 1 dimensional non linear Boltzmann equations with both Maxwell particles intermolecular forces and outside forces. We find exact solutions with a structure similar to the homogeneous Bobylev-Krook-Wu distributions. However, on the one hand, unlike the Bobylev inhomogeneous solution which corresponds to a gas in expansion, here these solutions can relax towards absolute Maxwellians. On the other hand, we construct also a class of exact inhomogeneous distributions relaxing towards different oscillating Maxwellians. Two types of external forces are handled: linear spatial forces (mainly harmonic potentials) and linear velocity forces plus uniform source term
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Source
Nov 1985; 7 p; R.C.P. 266 Meeting on inverse problems; Montpellier (France); 27-30 Nov 1985; SPHT--86-023
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AbstractAbstract
[en] We consider a four-velocity discrete and unidimensional Boltzmann model. The mass, momentum and energy conservation laws being satisfied we can define a temperature. We report the exact positive solutions which have been found: periodic in the space and propagating or not when the time is growing, shock waves similarity solutions and (1 + 1)-dimensional solutions
[fr]
Nous considerons un modele de Boltzmann unidimensionnel a quatre vitesses. Ce modele, satisfaisant trois lois de conservation de la masse du moment et de l'energie, permet de definir une temperature. Pour ce modele des solutions exactes positives existent: solutions periodiques dans l'espace se propageant ou non lorsque le temps varie, solutions de similarite d'ondes de choc et solutions a 1 + 1 dimensionsOriginal Title
Solutions exactes pour un modele de Boltzmann discretise unidimensionnel satisfaisant a toutes les lois de conservation
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Journal Article
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Comptes Rendus de l'Academie des Sciences, Serie 2; ISSN 0764-4450;
; CODEN CRAME; v. 309(19); p. 1883-1888

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AbstractAbstract
[en] The case of multiple collisions in the discrete Boltzmann equation is considered. We establish sufficient conditions to be verified by the discrete models of the Boltzmann equation, so that the one-dimensional initial value problem possesses a global solution in time, under the constraint that the initial densities and initial mass are positive and bounded
[fr]
Les collisions multiples etant prises en compte, on etablit des conditions suffisantes, que doivent verifier les modeles discrets de l'equation de Boltzmann, pour que le probleme unidimensionnel aux valeurs initiales possede une solution globale en temps, lorsque les densites et la masse initiales sont positives et borneesOriginal Title
Solution globale de l'equation de Boltzmann discrete avec collisions multiples
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Journal Article
Journal
Comptes Rendus de l'Academie des Sciences. Serie 1; ISSN 0764-4442;
; CODEN CASME; v. 313(3); p. 143-148

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