Abstract:
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.
Citation:
A. S. Ivanova, M. F. Pavlova, “On unique solvability of one nonlinear nonlocal with respect to a gradient solution of a nonstationary problem”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 3, 78–83; Russian Math. (Iz. VUZ), 61:3 (2017), 67–71
\Bibitem{IvaPav17}
\by A.~S.~Ivanova, M.~F.~Pavlova
\paper On unique solvability of one nonlinear nonlocal with respect to a gradient solution of a nonstationary problem
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2017
\issue 3
\pages 78--83
\mathnet{http://mi.mathnet.ru/ivm9219}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2017
\vol 61
\issue 3
\pages 67--71
\crossref{https://doi.org/10.3103/S1066369X17030082}
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Linking options:
https://www.mathnet.ru/eng/ivm9219
https://www.mathnet.ru/eng/ivm/y2017/i3/p78
This publication is cited in the following 1 articles:
O. V. Glazyrina, R. Z. Dautov, E. Y. Myagkova, “Implicit Finite Element Scheme with a Penalty for a Nonlocal Parabolic Obstacle Problem of Kirchhoff Type”, Lobachevskii J Math, 44:7 (2023), 2675
Citation in format AMSBIB
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