Local stability of spike steady states in a simplified Gierer-Meinhardt system
| dc.contributor.author | Karadzhov, Georgi E. | |
| dc.contributor.author | Edmunds, David E. | |
| dc.contributor.author | de Groen, Pieter P. N. | |
| dc.date.accessioned | 2021-05-24T17:54:15Z | |
| dc.date.available | 2021-05-24T17:54:15Z | |
| dc.date.issued | 2005-05-23 | |
| dc.description.abstract | In this paper we study the stability of the single internal spike solution of a simplified Gierer-Meinhardt' system of equations in one space dimension. The linearization around this spike consists of a selfadjoint differential operator plus a non-local term, which is a non-selfadjoint compact integral operator. We find the asymptotic behaviour of the small eigenvalues and we prove stability of the steady state for the parameter (p, q, r, μ) in a four-dimensional region (the same as for the shadow equation, [8]) and for any finite D if ε is sufficiently small. Moreover, there exists an exponentially large D(ε) such that the stability is still valid for D < D(ε). Thus we extend the previous results known only for the case r = p + 1 or r = 2, 1 < p < 5. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 22 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Karadzhov, G. E., Edmunds, D. E., & de Groen, P. P. N. (2005). Local stability of spike steady states in a simplified Gierer-Meinhardt system. <i>Electronic Journal of Differential Equations, 2005</i>(54), pp. 1-22. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13637 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Spike solution | |
| dc.subject | Singular perturbations | |
| dc.subject | Reaction-diffusion equations | |
| dc.subject | Gierer-Meinhardt equations | |
| dc.title | Local stability of spike steady states in a simplified Gierer-Meinhardt system | |
| dc.type | Article |