Asymptotic approximations for Green's function for the operator -Δ in a long rod are derived. These approximations are uniformly valid over the whole domain including the end regions of the rod. Connections are established between the asymptotic approximations in a long rod and the asymptotics in thin domains. Overview of asymptotic approximations of Green's kernels in a domain with a small hole and domains with singularly perturbed smooth or conical boundaries is also given. Copyright © 2008 John Wiley & Sons, Ltd.
CITATION STYLE
Maz’ya, V., & Movchan, A. (2008). Uniform asymptotic approximations of Green’s functions in a long rod. Mathematical Methods in the Applied Sciences, 31(17), 2055–2068. https://doi.org/10.1002/mma.1006
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