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MR1467460 (99j:35101) 35K57 (35B10 35B25)
Alikakos, Nicholas D.; Bates, Peter W.; Chen, Xinfu Periodic traveling waves and locating oscillating patterns in multidimensional domains. Trans. Amer. Math. Soc. 351 (1999), no. 7, 2777–2805.
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