## The detection of surface vibrations from interior acoustical pressure.(English)Zbl 1033.76053

This paper is devoted to the problem of identifying the source of the acoustic noise and the normal velocity of the sound on the surface of a three-dimensional domain $$\Omega$$. The acoustic field $$u$$ of frequency $$k$$ in $$\Omega$$ satisfies the Helmholtz equation $$\Delta u+k^2u =0$$ in $$\Omega$$. The authors show that any regular solution of this equation admits a unique representation by a single-layer potential, so that the problem is equivalent to the solution of linear integral equation of the first kind. Moreover, they develop a boundary element code to solve the integral equation.

### MSC:

 76Q05 Hydro- and aero-acoustics 76M15 Boundary element methods applied to problems in fluid mechanics 35R30 Inverse problems for PDEs 65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
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