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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 3, Pages 78–83 (Mi ivm9219)  
This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

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

A. S. Ivanova, M. F. Pavlova

Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
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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.
Keywords: parabolic equation, strongly monotone operator, nonlocal operator, generalized solution, solvability, uniqueness.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-05686_а
15-01-02315
Received: 26.08.2016
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, Volume 61, Issue 3, Pages 67–71
DOI: https://doi.org/10.3103/S1066369X17030082
Bibliographic databases:
Document Type: Article
UDC: 517.63
Language: Russian
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
Citation in format AMSBIB
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\paper On unique solvability of one nonlinear nonlocal with respect to a gradient solution of a nonstationary problem
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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