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Wei, Juncheng; Winter, Matthias

Spikes for the Gierer-Meinhardt system in two dimensions: the strong coupling case. (English) Zbl 1042.35005

J. Differ. Equations 178, No. 2, 478-518 (2002).
The authors deal with the study of the Gierer-Meinhardt system which models biological pattern formation. Numerical computations often low that the Gierer-Meinhardt system has stable solutions which display patterns of multiple interior peaks. Here the authors rigorously establish the existence and stability of such solutions of the full Gierer-Meinhardt system in two dimensions far from homogenity. To this end Green’s function together with its derivatives play a major role.
Reviewer: Messoud A. Efendiev (Berlin)

Cited in 54 Documents

MSC:

35B35 Stability in context of PDEs
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35K55 Nonlinear parabolic equations
35Q80 Applications of PDE in areas other than physics (MSC2000)
92C15 Developmental biology, pattern formation

Keywords:

pattern formation; strong coupling; interior peaks; stability
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\textit{J. Wei} and \textit{M. Winter}, J. Differ. Equations 178, No. 2, 478--518 (2002; Zbl 1042.35005)
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