Communications in Mathematical Sciences

Volume 11 (2013)

Number 1

Wave propagation in waveguides with random boundaries

Pages: 233 – 267



Ricardo Alonso (Computational and Applied Mathematics, Rice University, Houston, Texas, U.S.A.)

Liliana Borcea (Computational and Applied Mathematics, Rice University, Houston, Texas, U.S.A.)

Josselin Garnier (Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris VII, Paris, France)


We give a detailed analysis of long range cumulative scattering effects from rough boundaries in waveguides. We assume small random fluctuations of the boundaries and obtain a quantitative statistical description of the wave field. The method of solution is based on coordinate changes that straighten the boundaries. The resulting problem is similar from the mathematical point of view to that of wave propagation in random waveguides with interior inhomogeneities. We quantify the net effect of scattering at the random boundaries and show how it differs from that of scattering by internal inhomogeneities.


waveguides, random media, asymptotic analysis

2010 Mathematics Subject Classification

35Qxx, 60F05, 76B15

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