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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 14
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 14, Issue 5-6, December 2007
  4. Symmetric and asymmetric multiple clusters in a reaction-diffusion system
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 14, Issue 5-6, December 2007
Homogenization and behaviour of optimal controls for the wave equation in domains with oscillating boundary
On the exact limit cycle for some class of planar differential systems
A bifurcation problem governed by the boundary condition I
A bisection algorithm for the numerical Mountain Pass
Global bifurcation result for Dirichlet and Neumann p-biharmonic problem
Global bifurcation and multiplicity results for Sturm-Liouville problems
Stability of front tracking solutions to the initial and boundary value problem for systems of conservation laws
Well-posedness of a quasilinear hyperbolic-parabolic system arising in mathematical biology
The Cauchy problem for the 1-D Dirac–Klein–Gordon equation
Asymptotic behavior for Timoshenko beams subject to a single nonlinear feedback control
Experimental results for the Poincaré center problem
A remark on the junction in a thin multi-domain: the non convex case
A Landesman-Lazer type condition for a nonlinear Stekloff Problem
On very weak solutions of degenerate p-harmonic equations
A new proof of partial regularity of solutions to Navier-Stokes equations
Symmetric and asymmetric multiple clusters in a reaction-diffusion system
BSDE on an infinite horizon and elliptic PDEs in infinite dimension
Nonlinear Differential Equations and Applications NoDEA : Volume 14, Issue 3-4, November 2007
Nonlinear Differential Equations and Applications NoDEA : Volume 14, Issue 1-2, October 2007
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Symmetric and asymmetric multiple clusters in a reaction-diffusion system

Content Provider SpringerLink
Author Wei, Juncheng Winter, Matthias
Copyright Year 2007
Abstract We consider the following Gierer-Meinhardt system in R: $$\left\{\begin{array}{l} {\epsilon ^2 A'' - A + \frac{{A^2 }} {H} = 0,\quad x \in ( - 1,1),} \\ {DH'' - H + A^2 = 0,\quad x \in ( - 1,1),} \\ {A'( - 1) = A'(1) = H'( - 1) = H'(1) = 0,} \\ \end{array}\right. $$ where ε > 0 is a small parameter and D > 0 is a constant independent of ε.A cluster is a combination of several spikes concentrating at the same point. In this paper, we rigorously show the existence of symmetric and asymmetric multiple clusters. This result is new for systems and seems not to occur for single equations. We reduce the problem to the computation of two matrices which depend on the coefficient D as well as the number of different clusters and the number of spikes within each cluster.
Ending Page 823
Page Count 37
Starting Page 787
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 5
Volume Number 14
Language English
Publisher SP Birkhäuser Verlag Basel
Publisher Date 2007-12-19
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword singular perturbation Analysis Developmental biology, pattern formation turing instability Multiple clusters Reaction-diffusion equations Nonlinear elliptic equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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