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, 2020, Volume 32, Issue 3, Pages 149–179 (Mi aa1703)  
Research Papers

The leading edge of a free boundary interacting with a line of fast diffusion

L. A. Caffarellia, J.-M. Roquejoffreb

a The University of Texas at Austin, Mathematics Department RLM 8.100, 2515 Speedway Stop C1200, Austin, Texas 78712-1202, U.S.A.
b Institut de Mathématiques de Toulouse (UMR CNRS 5219), Université Toulouse III, 118 route de Narbonne, 31062 Toulouse cedex, France
Full-text PDF (342 kB)
References:
PDF
HTML
Abstract: The goal of this work is to explain an unexpected feature of the expanding level sets of the solutions of a system where a half-plane in which reaction-diffusion phenomena take place exchanges mass with a line having a large diffusion of its own. The system was proposed by H. Berestycki, L. Rossi and the second author as a model of enhancement of biological invasions by a line of fast diffusion. It was observed numerically by A.-C. Coulon that the leading edge of the front, rather than being located on the line, was in the lower half-plane.
We explain this behavior for a closely related free boundary problem. We construct travelling waves for this problem, and the analysis of their free boundary near the line confirms the predictions of the numerical simulations.
Keywords: expanding level sets, reaction-diffusion phenomena, line of fast diffusion.
Funding agency Grant number
National Science Foundation DMS-1160802
European Union's Seventh Framework Programme 321186
L. A. Caffarelli is supported by NSF grant DMS-1160802. The research of J.-M. Roquejoffre has received funding from the ERC under the European Union's Seventh Frame work Programme (FP/2007-2013) / ERC Grant Agreement 321186 — ReaDi.
Received: 29.07.2019
English version:
St. Petersburg Mathematical Journal, 2021, Volume 32, Issue 3, Pages 499–522
DOI: https://doi.org/10.1090/spmj/1658
Document Type: Article
Language: English
Citation: L. A. Caffarelli, J.-M. Roquejoffre, “The leading edge of a free boundary interacting with a line of fast diffusion”, Algebra i Analiz, 32:3 (2020), 149–179; St. Petersburg Math. J., 32:3 (2021), 499–522
Citation in format AMSBIB
\Bibitem{CafRoq20}
\by L.~A.~Caffarelli, J.-M.~Roquejoffre
\paper The leading edge of a free boundary interacting with a line of fast diffusion
\jour Algebra i Analiz
\yr 2020
\vol 32
\issue 3
\pages 149--179
\mathnet{http://mi.mathnet.ru/aa1703}
\transl
\jour St. Petersburg Math. J.
\yr 2021
\vol 32
\issue 3
\pages 499--522
\crossref{https://doi.org/10.1090/spmj/1658}
Linking options:
  • https://www.mathnet.ru/eng/aa1703
  • https://www.mathnet.ru/eng/aa/v32/i3/p149
    • 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
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024