Spherically symmetric internal layers for activator-inhibitor systems—I. Existence by a Lyapunov-Schmidt reduction |
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| Authors: | Kunimochi Sakamoto Hiromasa Suzuki |
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| Institution: | a Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan
b Department of Mathematics, Division of Education, Faculty of Education, Shiga University, Hiratsu, Otsu, 520-0862, Japan |
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| Abstract: | Reaction-diffusion systems of activator-inhibitor type are studied on an N-dimensional ball with the homogeneous Neumann boundary conditions. Under the condition that the activator diffuses slowly, reacts rapidly and the inhibitor diffuses rapidly, reacts moderately, we show that the system admits a family of spherically symmetric internal transition layer equilibria. The method of proof consists of rigorous asymptotic expansions and a Lyapunov-Schmidt reduction. |
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| Keywords: | 35B25 35B35 35K57 35R35 |
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