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Boundary Value Problems of Helmholtz Equation

In: Mathematical Foundation of the Boundary Integro-Differential Equation Method

Author

Listed:
  • Houde Han

    (Tsinghua University, Department of Mathematical Sciences)

  • Dongsheng Yin

    (Tsinghua University, Department of Mathematical Sciences)

Abstract

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 $$\rho _0$$ ρ 0 , speed of sound $$c_0$$ c 0 and damping coefficient $$\gamma _0$$ γ 0 in $$ \mathbb R^n$$ R n ( $$n=2, \, 3$$ n = 2 , 3 ), where the constant $$\rho _0>0, c_0>0$$ ρ 0 > 0 , c 0 > 0 and $$\gamma _0\geqslant 0$$ γ 0 ⩾ 0 .

Suggested Citation

  • Houde Han & Dongsheng Yin, 2026. "Boundary Value Problems of Helmholtz Equation," Springer Books, in: Mathematical Foundation of the Boundary Integro-Differential Equation Method, chapter 0, pages 129-187, Springer.
    • Handle: RePEc:spr:sprchp:978-981-95-1088-7_5
    DOI: 10.1007/978-981-95-1088-7_5
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