Geodesic
On stability in $\ell_p$ of some difference schemes for the transport equation
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 3, pp. 199-214

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In the present work, the stability in the space $\ell_p$, $1$, for a wide class of difference analogs of kinetic transport as well as for the Carleman nonlinear system in the Baltazar equation theory has been proved. The stability in the norm of the space $\ell_p$ results, as a particular case, in the stability in $\ell_2$, which coincides with the stability in the energy space, and at $p=\infty$, with the norm in the space $C$. In this case, the result is gained in the manner similar to the methods of obtaining a priori estimations in the norm of the space $L_p$ for differential problems by themselves. 
@article{SJVM_2002_5_3_a0,
     author = {A. Sh. Akysh (Akishev)},
     title = {On stability in $\ell_p$ of some difference schemes for the transport equation},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {199--214},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2002_5_3_a0/}
}
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A. Sh. Akysh (Akishev). On stability in $\ell_p$ of some difference schemes for the transport equation. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 3, pp. 199-214. http://geodesic.mathdoc.fr/item/SJVM_2002_5_3_a0/