Geodesic
On the solvability of the problem of the coupled movement of underground and surface waters with nonhomogeneous bounds to the solution
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 1, pp. 147-161

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We consider the problem that belongs to the class of problems with double degeneration. The main characteristic of this problem is a nonlocal boundary condition on the slit of the domain. By using the semidiscretization and penalty methods the theorem of the solvability of the first boundary condition problem for the corresponding variational inequality with nonhomogeneous bounds to the solution is proved.
Keywords: double degeneration, nonlocal boundary conditions, semidiscretization method, penalty method, generalized solution. 
@article{UZKU_2012_154_1_a12,
     author = {L. L. Glazyrina and M. F. Pavlova},
     title = {On the solvability of the problem of the coupled movement of underground and surface waters with nonhomogeneous bounds to the solution},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {147--161},
     publisher = {mathdoc},
     volume = {154},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_1_a12/}
}
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L. L. Glazyrina; M. F. Pavlova. On the solvability of the problem of the coupled movement of underground and surface waters with nonhomogeneous bounds to the solution. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 1, pp. 147-161. http://geodesic.mathdoc.fr/item/UZKU_2012_154_1_a12/