By Armand Wirgin (Ed.)

ISBN-10: 981238264X

ISBN-13: 9789812382641

Goal identity in noisy environments, L. Borcea et al; decision of the parameters of cancellous bone utilizing low frequency acoustic measurements, J.L. Buchanan et al; an inverse spectral challenge for a Schrodinger operator with an unbounded strength, L. Cardoulis et al; homogenizing the acoustic homes of a porous matrix containing an incompressible inviscid fluid, T. Clopeau and A. Mickelic; hardy areas of harmonic and monogenic features, R. Delanghe; a version for porous ductile viscoplastic solids together with void form results, L. Flandi and J.-B. Leblond; acoustic wave propagation in a composite of 2 various poro-elastic fabrics with a truly tough periodic interface - a homogenisation process, R.P. Gilbert and M.-J. Y. Ou; summability of ideas of Dirichlet challenge for a few degenerate nonlinear high-order equations with right-hand aspects in a logarithmic classification, A. Kovalevsky and F. Nicolosi; on isophonic surfaces, R. Magnanini and S. Sakaguchi; wignerization of caustics, G. Makrakis; at the managed evolution of point units and prefer tools in scalar inverse scattering, C. Ramananjaona et al; at the Brezis and Mironescu conjecture a couple of Gagliardo-Nirenberg inequality for fractional Sobolev norms, T. Shaposhnikova; seismic reaction of a chain of constructions (city) anchored in gentle soil, C. Tsogka and A. Wirgin. (Part contents)

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**Additional info for Acoustics, Mechanics, and the Related Topics of Mathematical Analysis: CAES du CNRS, Frejus, France, 18-22 June 2002**

**Sample text**

Acoust. Am. 59, 368-373 (1976). 4. A. B. Baggeroer, W. A. Kuperman, and H. Schmidt, “Matched field processing: Source localization in correlated noise as an optimum parameter estimation problem,” J. Acoust. Am. 83, 571-587 (1988). 5. F. B. Jensen, W. A. Kuperman, M. B. Porter, and H. Schmidt, Computational Ocean Acoustics (AIP Press, New York, 1994). 6. C. Prada and M. Fink, “Eigenmodes of the time reversal operator: A solution to selective focusing in multiple-target media,” Wave Motion 20, 151-163 (1994).

2. Uniqueness Let (E,H,u) be a solution of (CIP) corresponding to EiVac = Hinc = 0 . We denote by RR := Ren{ x E It3;1x1 < R } the annual region with dRR = I? U SR. We assume that the radius R is sufficiently large so that 52i is completely contained in SR. Applying the divergence theorem for E, E, H , H and using the transmission conditions we obtain ii x E . H ds + k2 (lkI21Hl2- k21EI2)dx = i k We consider the following cases: 1) k and w2 are real. Hds) =k,(L’Ih-iids), since is real. From the Silver-Muller radiation condition and (15) (see 2, it follows whence from Rellich’s lemma H = E G 0 in A*u+piw2u=0 Tu=O and fie.

The duct without the plate is noted fl (see Fig. 1). We restricted 4 g=h A’ a0 wave guide Figure 1. Geometry of the problem ourselves to the case of a plate placed in the center of the duct and to antisymmetric vibrations of the fluid with respect to the plate. 1. Fluid The velocity of the uniform flow is noted U. In time harmonic regime of frequency w , the linearized Euler’s equations lead to the ”convected” Helmholtz equation for the velocity potential 4 : U < C W 1 is the Mach number, c the sound velocity and k = - the C acoustic wavenumber, which will be called frequency in the sequel.

### Acoustics, Mechanics, and the Related Topics of Mathematical Analysis: CAES du CNRS, Frejus, France, 18-22 June 2002 by Armand Wirgin (Ed.)

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