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Algebra i Analiz, 2013, Volume 25, Issue 4, Pages 47–84 (Mi aa1344)  

This article is cited in 4 scientific papers (total in 4 papers)

Research Papers

On blowup dynamics in the Keller–Segel model of chemotaxis

S. I. Dejaka, D. Eglia, P. M. Lushnikovb, I. M. Sigala

a University of Toronto, Department of Mathematics, Toronto, Canada
b University of New Mexico, Department of Mathematics and Statistics, USA

Abstract: The (reduced) Keller–Segel equations modeling chemotaxis of bio-organisms are investigated. A formal derivation and partial rigorous results of the blowup dynamics are presented for solutions of these equations describing the chemotactic aggregation of the organisms. The results are confirmed by numerical simulations, and the formula derived coincides with the formula of Herrero and Velázquez for specially constructed solutions.

Keywords: reaction-diffusion equations, nonlinear partial differential equations, blowup, collapse, chemotaxis, Keller–Segel equation, blowup profile.

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English version:
St. Petersburg Mathematical Journal, 2014, 25:4, 547–574

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Received: 01.12.2012
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Citation: S. I. Dejak, D. Egli, P. M. Lushnikov, I. M. Sigal, “On blowup dynamics in the Keller–Segel model of chemotaxis”, Algebra i Analiz, 25:4 (2013), 47–84; St. Petersburg Math. J., 25:4 (2014), 547–574

Citation in format AMSBIB
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\vol 25
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\pages 47--84
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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. S. A. Dyachenko, P. M. Lushnikov, N. Vladimirova, “Logarithmic scaling of the collapse in the critical Keller-Segel equation”, Nonlinearity, 26:11 (2013), 3011–3041  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. A. Blanchet, J. A. Carrillo, D. Kinderlehrer, M. Kowalczyk, Ph. Laurençot, S. Lisini, “A hybrid variational principle for the Keller-Segel system in $\mathbb R^2$”, ESAIM Math. Model. Numer. Anal., 49:6 (2015), 1553–1576  crossref  mathscinet  zmath  isi  scopus
    3. Azevedo J., Cuevas C., Henriquez E., “Existence and Asymptotic Behaviour For the Time-Fractional Keller-Segel Model For Chemotaxis”, Math. Nachr., 292:3 (2019), 462–480  crossref  mathscinet  zmath  isi  scopus
    4. Juengel A., Leingang O., “Blow-Up of Solutions to Semi-Discrete Parabolic-Elliptic Keller-Segel Models”, Discrete Contin. Dyn. Syst.-Ser. B, 24:9 (2019), 4755–4782  crossref  isi
  • Алгебра и анализ St. Petersburg Mathematical Journal
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