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

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Abstract

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.

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    A. S. Ivanova & M. F. Pavlova

Authors
  1. A. S. Ivanova
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  2. M. F. Pavlova
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Corresponding author

Correspondence to A. S. Ivanova.

Additional information

Original Russian Text © A.S. Ivanova, M.F. Pavlova, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 3, pp. 78–83.

Submitted by R.Z. Dautov

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Ivanova, A.S., Pavlova, M.F. On unique solvability of one nonlinear nonlocal with respect to the solution gradient nonstationary problem. Russ Math. 61, 67–71 (2017). https://doi.org/10.3103/S1066369X17030082

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  • DOI: https://doi.org/10.3103/S1066369X17030082

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