Exponential Estimates in Averaging and Homogenisation

Karsten Matthies ()
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Karsten Matthies: University of Bath, Department of Mathematical Sciences

A chapter in Analysis, Modeling and Simulation of Multiscale Problems, 2006, pp 1-19 from Springer

Abstract: Summary Many partial differential equations with rapid spatial or temporal scales have effective descriptions which can be derived by homogenisation or averaging. In this article we deal with examples, where quantitative estimates of the error is possible for higher order homogenisation and averaging. In particular, we provide theorems, which allow homogenisation and averaging beyond all orders by giving exponential estimates of appropriately averaged and homogenised descriptions. Methods include iterated averaging transformations, optimal truncation of asymptotic expansions and highly regular solutions (Gevrey regularity). Prototypical examples are reaction-diffusion equations with heterogeneous reaction terms or rapid external forcing, nonlinear Schrödinger equations describing dispersion management, and second-order linear elliptic equations.

Keywords: Normal Form; Unstable Manifold; Homoclinic Orbit; Remainder Term; Approximation Space (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-35657-8_1

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DOI: 10.1007/3-540-35657-6_1

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