Abstract
We consider a nonlinear degenerate parabolic equation whose spatial operator depends on a nonlocal characteristic of the solution. We prove the uniqueness of the solution in the class of vector-valued functions that take on values in Sobolev spaces.
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References
M. Chipot and L. Molinet, “Asymptotic Behavior of Some Nonlocal Diffusion Problems,” Appl. Anal. 80(3/4), 279–315 (2001).
M. F. Pavlova, “On the Solvability of Nonlocal Nonstationary Problems with Double Degeneration,” Differents. Uravn. 47(8), 1148–1163 (2001).
M. Chipot and B. Lovat, “Existence and Uniqueness Results for a Class of Nonlocal Elliptic Problems, Advances in Quenching,” Dyn. Contin. Discrete Impuls. Syst., Ser. A,Math. Anal. 195(1), 14–24 (2001).
M. M. Karchevskii and M. F. Pavlova, Equations of Mathematical Physics (Kazansk. Gos. Univ., Kazan, 2008) [in Russian].
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Original Russian Text © O.V. Glazyrina and M.F. Pavlova, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 3, pp. 92–95.
Submitted by R. Z. Dautov
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Glazyrina, O.V., Pavlova, M.F. The unique solvability of a certain nonlocal nonlinear problem with a spatial operator strongly monotone with respect to the gradient. Russ Math. 56, 83–86 (2012). https://doi.org/10.3103/S1066369X12030103
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DOI: https://doi.org/10.3103/S1066369X12030103