Boundary Value Problems of Helmholtz Equation

Houde Han () and Dongsheng Yin ()
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Houde Han: Tsinghua University, Department of Mathematical Sciences
Dongsheng Yin: Tsinghua University, Department of Mathematical Sciences

Chapter Chapter 5 in Mathematical Foundation of the Boundary Integro-Differential Equation Method, 2026, pp 129-187 from Springer

Abstract: 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 .

Date: 2026
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DOI: 10.1007/978-981-95-1088-7_5

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