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  • 1
    Digitale Medien
    Digitale Medien
    Generalized solutions of the radiative transfer equations in a singular case (1986)
    Springer
    Communications in mathematical physics 106 (1986), S. 211-239 
    Details
    ISSN: 1432-0916
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: Abstract This paper is devoted to the study of the radiative transfer equations: First, we prove a global existence theorem, which allows a blow-up of the opacity σv(ℰ) when ℰ→0. Thus, it extends Mercier's previous result [13]. This proof relies mainly on a nonlinear version of Hille-Yosida theorem: see Crandall-Ligett [9]. Then, we prove the uniqueness of the semigroup solving (TR), and some regularity results (in the class of functions with bounded variation). Finally, we prove the convergence of some splitting algorithms associated to (TR).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01454973
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  • 2
    Digitale Medien
    Digitale Medien
    On the mean free path for a periodic array of spherical obstacles (1996)
    Springer
    Journal of statistical physics 82 (1996), S. 1385-1407 
    Details
    ISSN: 1572-9613
    Schlagwort(e): Lorentz gas ; kinetic theory ; mean free path ; continued fractions ; ergodization rate ; small divisors
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We prove theorems pertaining to periodic arrays of spherical, obstacles which show how the macroscopic limit of the mean free path depends on the scaling of the size of the obstacles. We treat separately the cases where the obstacles are totally and partially absorbing, and we also distinguish between two-dimensional arrays, where our results are optimal, and higher dimensional arrays, where they are not. The cubically symmetric arrays to which these results apply do not have finite horizon.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02183388
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  • 3
    Digitale Medien
    Digitale Medien
    Remarks on the notion of mean free path for a periodic array of spherical obstacles (1997)
    Springer
    Journal of statistical physics 87 (1997), S. 943-950 
    Details
    ISSN: 1572-9613
    Schlagwort(e): Mean free path ; dispersive billiards ; periodic Lorentz gas ; kinetic theory ; ext time ; homogenization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract In this note, we explain in detail how the notion of mean free path is related to the mathematical results obtained in our previous paper.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02181255
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  • 4
    Digitale Medien
    Digitale Medien
    Stationary solutions of the linearized Boltzmann equation in a half-space (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 483-502 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Stationary half-space solutions of the linearized Boltzmann equation are studied by energy estimates methods. We extend the results of Bardos, Caflisch and Nicolaenko for a gas of hard spheres to a general potential. Asymptotic behaviour is obtained for hard as well as soft potentials and compared to the case of hard spheres.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670110406
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