Smoke-ring Solutions of Gierer-meinhardt System in R
نویسندگان
چکیده
with an additional restriction q = p − 1. In the limit ε → 0, we use formal asymptotics to construct a solution whose activator component a concentrates on a circle. Under additional constraints p > 1, m > 0, and 1 < m − s < 3, we find that such a solution exists and is unique. The radius of the circle of concentration is given explicitly in terms of certain integrals. Full numerical computations are shown to support analytical results.
منابع مشابه
Smoke-Ring Solutions of Gierer-Meinhardt System in R3
Abstract. We consider the steady states of the Gierer–Meinhardt system on all of R: εΔa − a + a hq = 0, Δh − h + a hs = 0 with an additional restriction q = p − 1. In the limit ε → 0, we use formal asymptotics to construct a solution whose activator component a concentrates on a circle. Under the additional constraints p > 1, m > 0, and 1 < m− s < 3, we find that such a solution exists and is u...
متن کاملIdentification of Space-Time Distributed Parameters in the Gierer-Meinhardt Reaction-Diffusion System
We consider parameter identification for the classic Gierer-Meinhardt reactiondiffusion system. The original Gierer-Meinhardt model [A. Gierer and H. Meinhardt, Kybernetik, 12 (1972), pp. 30-39] was formulated with constant parameters and has been used as a prototype system for investigating pattern formation in developmental biology. In our paper the parameters are extended in time and space a...
متن کاملSpikes for the Gierer-meinhardt System in Two Dimensions: the Strong Coupling Case
Numerical computations often show that the Gierer-Meinhardt system has stable solutions which display patterns of multiple interior peaks (often also called spots). These patterns are also frequently observed in natural biological systems. It is assumed that the diffusion rate of the activator is very small and the diffusion rate of the inhibitor is finite (this is the so-called strong-coupling...
متن کاملSpikes for the Two-dimensional Gierer-meinhardt System: the Strong Coupling Case
Numerical computations often show that the Gierer-Meinhardt system has stable solutions which display patterns of multiple interior peaks (often also called spots). These patterns are also frequently observed in natural biological systems. It is assumed that the diiusion rate of the activator is very small and the diiusion rate of the inhibitor is nite (this is the so-called strong-coupling cas...
متن کاملOn Single Interior Spike Solutions of Gierer-meinhardt System: Uniqueness and Spectrum Estimates
We study the interior spike solutions to a steady state problem of the shadow system of the Gierer-Meinhardt system arising from biological pattern formation. We rst show that at a nondegenerate peak point the interior spike solution is locally unique and then we establish the spectrum estimates of the associated linearized operator. We also prove that the corresponding solution to the shadow s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011