Geodesic
Difference solutions of a class of quasilinear parabolic equations. I
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 3, pp. 646-659

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The properties of implicit difference schemes for quasilinear parabolic equations of non-linear heat conduction with a source are investigated. The sufficient conditions for the scheme to be solvable, for a difference solution to be non-unique and non-existent, and also for its unlimited increase over a finite time, are determined. 
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     author = {V. A. Galaktionov and A. A. Samarskii},
     title = {Difference solutions of a class of quasilinear parabolic {equations.~I}},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {646--659},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_3_a12/}
}
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V. A. Galaktionov; A. A. Samarskii. Difference solutions of a class of quasilinear parabolic equations. I. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 3, pp. 646-659. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_3_a12/