Geodesic
Research on the convergence of an explicit difference scheme for a parabolic equation with a nonlinear nonlocal spatial operator
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 4, pp. 24-39

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We consider the first boundary value problem for a parabolic equation with a spatial operator degenerating with respect to the gradient. This operator also depends on the integral characteristic of the solution. We prove the convergence theorem for an explicit difference scheme under minimal assumptions on the smoothness of the initial data.
Mots-clés : parabolic equations, convergence.
Keywords: monotone operator, nonlocal operator, explicit difference scheme, stability 
@article{UZKU_2013_155_4_a2,
     author = {O. V. Glazyrina and M. F. Pavlova},
     title = {Research on the convergence of an explicit difference scheme for a~parabolic equation with a~nonlinear nonlocal spatial operator},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {24--39},
     publisher = {mathdoc},
     volume = {155},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2013_155_4_a2/}
}
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O. V. Glazyrina; M. F. Pavlova. Research on the convergence of an explicit difference scheme for a parabolic equation with a nonlinear nonlocal spatial operator. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 4, pp. 24-39. http://geodesic.mathdoc.fr/item/UZKU_2013_155_4_a2/