Homogenisation of exponential order for elliptic systems in infinite cylinders

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Abstract

We consider systems of semilinear elliptic equations on infinite cylinders with a nonlinear rapid periodic inhomogeneity in the unbounded direction. We transform the equation, such that the inhomogeneous term is exponentially small in the period of the inhomogeneity for bounded solutions. The results can be used to show that equilibrium solutions persist as periodic solutions with exponentially small modulation. The analytic tools of the paper include the dynamical systems approach to elliptic equations, averaging of exponential order for ordinary differential equations and extreme regularity (Gevrey classes).
Original languageEnglish
Pages (from-to)205-232
JournalAsymptotic Analysis
Volume43
Issue number3
Early online date23 Jun 2005
Publication statusPublished - 2005

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