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Mat. Sb., 2018, Volume 209, Number 2, Pages 66–81 (Mi msb8850)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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).


DOI: https://doi.org/10.4213/sm8850

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English version:
Sbornik: Mathematics, 2018, 209:2, 206–221

Bibliographic databases:

Document Type: Article
UDC: 517.956.45+517.968.74
MSC: Primary 35K65; Secondary 35K55, 45K05
Received: 20.10.2016 and 05.04.2017

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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  • http://mi.mathnet.ru/eng/msb8850
  • https://doi.org/10.4213/sm8850
  • http://mi.mathnet.ru/eng/msb/v209/i2/p66

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. F. Vil'danova, “On uniqueness of weak solution to mixed problem for integro-differential aggregation equation”, Ufa Math. J., 10:4 (2018), 40–49  mathnet  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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