Highly oscillatory behavior of the activator in the Gierer and Meinhardt system |
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| Authors: | Patricio Felmer Salomé Martínez Kazunaga Tanaka |
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| Affiliation: | (1) Departamento de Ingeniería Matemática, Centro de Modelamiento Matemático, UMI2807 CNRS-UChile, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile;(2) Department of Mathematics, School of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan |
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| Abstract: | In this article we construct a new type of solutions for the Gierer and Meinhardt system with boundary conditions u x (0) = u x (L) = 0 and v x (0) = v x (L) = 0. As ε approaches zero, we construct a family of positive solution (u ε , v ε ) such that the activator u ε oscillates c 0/ε times, with c 0 in an appropriate range, while the inhibitor remains close to a limiting profile, which is a strictly decreasing function. |
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| Keywords: | KeywordHeading" >Mathematics Subject Classification (2000) 35B25 35J60 |
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