On unique solvability of one nonlinear nonlocal with respect to the solution gradient nonstationary problem

We consider a parabolic equation whose space operator is a product of a nonlinear bounded function which depends on a nonlocal characteristic with respect to a solution gradient and a 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. © 2017, Allerton Press, Inc.