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In this chapter, we discuss the boundary value problems of Helmholtz equation, which is from the time-harmonic acoustic scattering (Colton & Kress, 2013). Consider the acoustic wave propagation in a homogeneous isotropic medium with density \(\rho _0\) , speed of sound \(c_0\) and damping coefficient \(\gamma _0\) in \( \mathbb R^n\) ( \(n=2, \, 3\) ), where the constant \(\rho _0>0, c_0>0\) and \(\gamma _0\geqslant 0\) .

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Boundary Value Problems of Helmholtz Equation

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  • 发表日期：

    2026年

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  • Houde Han,
  • Dongsheng Yin

摘要

In this chapter, we discuss the boundary value problems of Helmholtz equation, which is from the time-harmonic acoustic scattering (Colton & Kress, 2013). Consider the acoustic wave propagation in a homogeneous isotropic medium with density \(\rho _0\) , speed of sound \(c_0\) and damping coefficient \(\gamma _0\) in \( \mathbb R^n\) ( \(n=2, \, 3\) ), where the constant \(\rho _0>0, c_0>0\) and \(\gamma _0\geqslant 0\) .