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).

title = "Homogenisation of exponential order for elliptic systems in infinite cylinders",

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).",

author = "Karsten Matthies",

year = "2005",

language = "English",

volume = "43",

pages = "205--232",

journal = "Asymptotic Analysis",

issn = "0921-7134",

publisher = "IOS Press",

number = "3",

}

TY - JOUR

T1 - Homogenisation of exponential order for elliptic systems in infinite cylinders

AU - Matthies, Karsten

PY - 2005

Y1 - 2005

N2 - 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).

AB - 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).

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