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. On deduces from this result a complete picture of the spectrum of Q in an Hilbert setting, generalizing results from Carleman to granular gases. From this integral representation of Q we also obtain that the semigroup associated to the linear Boltzmann equation for dissipative hard spheres is honest.
Integral representation of the linear Boltzmann operator for granular gas dynamics with applications
ARLOTTI, Luisa;
2007-01-01
Abstract
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. On deduces from this result a complete picture of the spectrum of Q in an Hilbert setting, generalizing results from Carleman to granular gases. From this integral representation of Q we also obtain that the semigroup associated to the linear Boltzmann equation for dissipative hard spheres is honest.File in questo prodotto:
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