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Homogenisation of Exponential Order for Elliptic Systems in Infinite Cylinders (2000)

by Karsten Matthies
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Abstract:

We consider systems of semilinear elliptic equations on infinite cylinders, where is 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, extreme regularity (Gevrey classes) and an abstract Cauchy-Kowalevsky theorem.

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