Geodesic
Global solutions of nonstationary kinetic equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 169-177

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For the nonstationary Boltzmann equation $$ \frac{\partial F}{\partial t}+\xi_\alpha\frac{\partial F}{\partial x_\alpha}=Q(F,F),\qquad t>0,\quad\xi\in R^3,\quad x\in\Omega\subset R^3, $$ one proves the unique global solvability of the Cauchy problem under nondifferentiable initial data and the unique global solvability of initial-boundary-value problems with homogeneous boundary conditions; it is shown that the solutions of the initial-boundary-value problems decay exponentially as $t\to\infty$. 
@article{ZNSL_1982_115_a13,
     author = {N. B. Maslova},
     title = {Global solutions of nonstationary kinetic equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {169--177},
     publisher = {mathdoc},
     volume = {115},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a13/}
}
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N. B. Maslova. Global solutions of nonstationary kinetic equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 169-177. http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a13/