期刊
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
卷 3, 期 3, 页码 419-439出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219199701000433
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In this paper we study ground-states of the Gierer & Meinhardt system on the line, namely solutions of the problem u - u + u(2)/v = 0, sigma (-2)v - v + u(2) = 0, u, v > 0, u(+/-infinity) = 0 = v(+/-infinity). We prove that given any number N, there exists a solution to this problem exhibiting exactly N bumps in its u-component, separated from each other at a distance O(\ log sigma\), whenever sigma is sufficiently small. These bumps resemble the shape of the unique solution of U - U + U-2 = 0, 0 < U(+/-) = 0, U'(0) = 0.
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