Algebra i Analiz
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Algebra i Analiz:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Algebra i Analiz, 2013, Volume 25, Issue 4, Pages 47–84 (Mi aa1344)  
This article is cited in 6 scientific papers (total in 6 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
Full-text PDF (380 kB) Citations (6)
References:
PDF
HTML
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.
Received: 01.12.2012
English version:
St. Petersburg Mathematical Journal, 2014, Volume 25, Issue 4, Pages 547–574
DOI: https://doi.org/10.1090/S1061-0022-2014-01306-4
Bibliographic databases:
Document Type: Article
Language: English
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
\Bibitem{DejEglLus13}
\by S.~I.~Dejak, D.~Egli, P.~M.~Lushnikov, I.~M.~Sigal
\paper On blowup dynamics in the Keller--Segel model of chemotaxis
\jour Algebra i Analiz
\yr 2013
\vol 25
\issue 4
\pages 47--84
\mathnet{http://mi.mathnet.ru/aa1344}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3184616}
\zmath{https://zbmath.org/?q=an:06373466}
\elib{https://elibrary.ru/item.asp?id=20730218}
\transl
\jour St. Petersburg Math. J.
\yr 2014
\vol 25
\issue 4
\pages 547--574
\crossref{https://doi.org/10.1090/S1061-0022-2014-01306-4}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000343074200004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84924452661}
Linking options:
  • https://www.mathnet.ru/eng/aa1344
  • https://www.mathnet.ru/eng/aa/v25/i4/p47
    • This publication is cited in the following 6 articles:
    1. Collot Ch., Ghoul T.-E., Masmoudi N., Nguyen V.T., “Spectral Analysis For Singularity Formation of the Two Dimensional Keller-Segel System”, Ann. PDE, 8:1 (2022), 5  crossref  mathscinet  isi
    2. Ray S.S., “Similarity Solutions For Keller-Segel Model With Fractional Diffusion of Cells”, Math. Meth. Appl. Sci., 44:10, SI (2021), 8379–8396  crossref  mathscinet  isi
    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  mathscinet  isi  scopus
    5. A. Blanchet, J. A. Carrillo, D. Kinderlehrer, M. Kowalczyk, Ph. Laurençot, S. Lisini, “A hybrid variational principle for the Keller-Segel system in R2”, ESAIM Math. Model. Numer. Anal., 49:6 (2015), 1553–1576  crossref  mathscinet  zmath  isi  scopus
    6. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
    Statistics & downloads:
    Abstract page:366
    Full-text PDF :84
    References:64
    First page:13
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025