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Existence , Classification and Stability Analysis of Multiple-peaked Solutions for the Gierer-meinhardt System in R
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wei, Juncheng Winter, Matthias |
| Copyright Year | 2008 |
| Abstract | We consider the following Gierer-Meinhardt system in R: At = 2A ′′ −A + A p Hq x ∈ (−1, 1), t > 0, τHt = DH ′′ −H + A r Hs x ∈ (−1, 1), t > 0, A ′ (−1) = A(1) = H (−1) = H (1) = 0, where (p, q, r, s) satisfy 1 < qr (s + 1)(p− 1) < +∞, 1 < p < +∞, and where 2 << 1, 0 < D < ∞, τ ≥ 0, D and τ are constants which are independent of 2. 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.. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.cuhk.edu.hk/~wei/Npeak1d8.pdf |
| Alternate Webpage(s) | http://www.math.ubc.ca/~jcwei/Npeak1d8.pdf |
| Alternate Webpage(s) | http://bura.brunel.ac.uk/bitstream/2438/2970/1/42-Npeak1d8.pdf |
| Alternate Webpage(s) | http://www.intlpress.com/site/pub/files/_fulltext/journals/maa/2007/0014/0002/MAA-2007-0014-0002-a002.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Coefficient Computation (action) |
| Content Type | Text |
| Resource Type | Article |
