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. 
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     title = {On unique solvability of one nonlinear nonlocal with respect to a gradient solution of a nonstationary problem},
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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/

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