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Sbornik: Mathematics, 2018, Volume 209, Issue 2, Pages 206–221
DOI: https://doi.org/10.1070/SM8850 (Mi sm8850) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Existence and uniqueness of a weak solution of a nonlocal aggregation equation with degenerate diffusion of general form

V. F. Vil'danova

Bashkir State Pedagogical University, Ufa
English version PDF (506 kB) Citations (5)
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DOI: https://doi.org/10.1070/SM8850
Abstract: The uniqueness of a weak solution of a nonlocal aggregation equation with degenerate diffusion is proved using the method of energy estimates. The existence of a solution is proved by combining the methods of iterations and contraction maps with the use of energy estimates. The equations under consideration arise in models of biological aggregation.
Bibliography: 23 titles.
Keywords: aggregation equation, uniqueness of a solution, existence of a solution.
Funding agency Grant number
Russian Foundation for Basic Research 17-41-020195 р_а
This research was supported by the Russian Foundation for Basic Research (grant no. 17-41-020195 р_а).
Received: 20.10.2016 and 05.04.2017
Russian version:
Matematicheskii Sbornik, 2018, Volume 209, Number 2, Pages 66–81
DOI: https://doi.org/10.4213/sm8850
Bibliographic databases:
Document Type: Article
UDC: 517.956.45+517.968.74
MSC: Primary 35K65; Secondary 35K55, 45K05
Language: English
Original paper language: Russian
Citation: V. F. Vil'danova, “Existence and uniqueness of a weak solution of a nonlocal aggregation equation with degenerate diffusion of general form”, Mat. Sb., 209:2 (2018), 66–81; Sb. Math., 209:2 (2018), 206–221
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:53
    First page:29
     
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