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Homogenisation of exponential order for elliptic systems in infinite cylinders


Reference:

Matthies, K., 2005. Homogenisation of exponential order for elliptic systems in infinite cylinders. Asymptotic Analysis, 43 (3), pp. 205-232.

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    Official URL:

    http://iospress.metapress.com/link.asp?id=upbv67hu5nvfqwd3

    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).

    Details

    Item Type Articles
    CreatorsMatthies, K.
    DepartmentsFaculty of Science > Mathematical Sciences
    RefereedYes
    StatusPublished
    ID Code7133

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