Expansion of the Linear Boltzmann Operator
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چکیده
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15 صفحه اولMathematical investigation of the Boltzmann collisional operator
With help of direct calculation, it is revealed that an essential concept in deriving the Boltzmann collisional operator, the scattering cross section in the laboratory frame, cannot be well defined. Along this line, it is suggested that the collisional operator, as well as the entire Boltzmann equation, should be reconsidered.
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We investigate the properties of the collision operator Q associated to the linear Boltzmann equation for dissipative hard-spheres arising in granular gas dynamics. We establish that, as in the case of non–dissipative interactions, the gain collision operator is an integral operator whose kernel is made explicit. One deduces from this result a complete picture of the spectrum of Q in an Hilbert...
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In this paper we study the integrability properties of a general version of the Boltzmann collision operator that includes inelastic interactions between particles. We prove a Young’s inequality for variable hard potentials, a Hardy-Littlewood-Sobolev inequality for soft potentials, and estimates with Maxwellian weights for variable hard potentials. In addition we obtain sharp constants for Max...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics
سال: 1961
ISSN: 0033-068X
DOI: 10.1143/ptp.25.1049