Geodesic
The unique solvability of a~certain nonlocal nonlinear problem with a~spatial operator strongly monotone with respect to the gradient
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2012), pp. 92-95

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We consider a nonlinear degenerate parabolic equation whose spatial operator depends on a nonlocal characteristic of the solution. We prove the uniqueness of the solution in the class of vector-valued functions that take on values in Sobolev spaces.
Mots-clés : parabolic equation
Keywords: monotone operator, nonlocal operator, uniqueness. 
@article{IVM_2012_3_a9,
     author = {O. V. Glyzarina and M. F. Pavlova},
     title = {The unique solvability of a~certain nonlocal nonlinear problem with a~spatial operator strongly monotone with respect to the gradient},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {92--95},
     publisher = {mathdoc},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_3_a9/}
}
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O. V. Glyzarina; M. F. Pavlova. The unique solvability of a~certain nonlocal nonlinear problem with a~spatial operator strongly monotone with respect to the gradient. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2012), pp. 92-95. http://geodesic.mathdoc.fr/item/IVM_2012_3_a9/