Geodesic
Existence and stability analysis for the Carleman kinetic system
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 12, pp. 2076-2087

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A global existence theorem for the discrete Carleman system in the Sobolev class $W^{1,2}$ is proved by the Leray–Schauder topological degree method, which was not previously applied to discrete kinetic equations. The instability of the nonequilibrium steady flow on a bounded interval is established in the linear approximation. 
@article{ZVMMF_2007_47_12_a8,
     author = {O. V. Ilyin},
     title = {Existence and stability analysis for the {Carleman} kinetic system},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2076--2087},
     publisher = {mathdoc},
     volume = {47},
     number = {12},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a8/}
}
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O. V. Ilyin. Existence and stability analysis for the Carleman kinetic system. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 12, pp. 2076-2087. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_12_a8/