Highly oscillatory behavior of the activator in the Gierer and Meinhardt system

Patricio Felmer, Salomé Martínez, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    In this article we construct a new type of solutions for the Gierer and Meinhardt system -ε2uxx + u &=&u 2/v in (0,L),- vxx+ v &=& u2 in (0, L) with boundary conditions u x (0) = u x (L) = 0 and v x (0) = v x (L) = 0. As ε approaches zero, we construct a family of positive solution (u ε , v ε ) such that the activator u ε oscillates c 0/ε times, with c 0 in an appropriate range, while the inhibitor remains close to a limiting profile, which is a strictly decreasing function.

    Original languageEnglish
    Pages (from-to)749-773
    Number of pages25
    JournalMathematische Annalen
    Volume340
    Issue number4
    DOIs
    Publication statusPublished - 2008 Apr

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    Inhibitor
    Positive Solution
    Strictly
    Limiting
    Boundary conditions
    Zero
    Range of data
    Profile
    Family

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Highly oscillatory behavior of the activator in the Gierer and Meinhardt system. / Felmer, Patricio; Martínez, Salomé; Tanaka, Kazunaga.

    In: Mathematische Annalen, Vol. 340, No. 4, 04.2008, p. 749-773.

    Research output: Contribution to journalArticle

    Felmer, Patricio ; Martínez, Salomé ; Tanaka, Kazunaga. / Highly oscillatory behavior of the activator in the Gierer and Meinhardt system. In: Mathematische Annalen. 2008 ; Vol. 340, No. 4. pp. 749-773.
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