Geodesic
On unique solvability of one nonlinear nonlocal with respect to a gradient solution of a nonstationary problem
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2017), pp. 78-83

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We consider a parabolic equation whose space operator is a product of nonlinear bounded function which depends on nonlocal characteristic with respect to a solution gradient and strongly monotone, potential operator. We prove the existence and uniqueness of the solution in the class of the vector-valued functions with values in the Sobolev space.
Mots-clés : parabolic equation
Keywords: strongly monotone operator, nonlocal operator, generalized solution, solvability, uniqueness. 
@article{IVM_2017_3_a7,
     author = {A. S. Ivanova and M. F. Pavlova},
     title = {On unique solvability of one nonlinear nonlocal with respect to a gradient solution of a nonstationary problem},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {78--83},
     publisher = {mathdoc},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_3_a7/}
}
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A. S. Ivanova; M. F. Pavlova. On unique solvability of one nonlinear nonlocal with respect to a gradient solution of a nonstationary problem. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2017), pp. 78-83. http://geodesic.mathdoc.fr/item/IVM_2017_3_a7/