Geodesic
Difference solutions of a class of quasilinear parabolic equations. II
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 4, pp. 831-838

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The properties of implicit difference schemes for quasi-linear parabolic equations of non-linear heat conduction with a source are studied. The sufficient conditions are found for the global solvability and uniqueness of the solution of the difference problem. It is shown that the global difference solution converges by a passage to the limit to the generalized solution of the initial differential problem. 
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     author = {V. A. Galaktionov and A. A. Samarskii},
     title = {Difference solutions of a class of quasilinear parabolic {equations.~II}},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {831--838},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_4_a5/}
}
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V. A. Galaktionov; A. A. Samarskii. Difference solutions of a class of quasilinear parabolic equations. II. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 4, pp. 831-838. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_4_a5/