Abstract. We consider the following Gierer-Meinhardt system in R 1 : and where << 1, 0 < D < ∞, τ ≥ 0, D and τ are constants which are independent of . We give a rigorous and unified approach to show that the existence and stability of N −peaked steady-states can be reduced to computing two matrices in terms of the coefficients D, N, p, q, r, s. Moreover, it is shown that N −peaked steady-states are generated by exactly two types of peaks, provided their mutual distance is bounded away from zero..
In REF the existence and stability of N−peaked steady states for the Gierer-Meinhardt system with precursor inhomogeneity has been explored.
EXISTENCE, CLASSIFICATION AND STABILITY ANALYSIS OF MULTIPLE-PEAKED SOLUTIONS FOR THE GIERER-MEINHARDT SYSTEM IN R
Methods and applications of analysis
Mathematics