Singular localised boundary-domain integral equations of acoustic scattering by inhomogeneous anisotropic obstacle
Singular localised boundary-domain integral equations of acoustic scattering by inhomogeneous anisotropic obstacle
复制标题
非均匀各向异性障碍物声散射的奇异局域边域积分方程
DOI：
10.1002/mma.5268
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发表时间：
2018
影响因子：
2.9
通讯作者：
Chkadua O
中科院分区：
文献类型：
--
作者：
Chkadua O
我们考虑嵌入无界各向异性均匀介质中有界各向异性非均匀介质的时谐声波散射。材料参数在不均匀的内部区域和均匀的外部区域之间的界面上可能具有不连续性。将相应的数学问题转化为具有间断变系数的二阶Helmholtz型椭圆型偏微分方程解的传输问题。利用基于调和基本解的局部化拟参数线，将频率参数任意取值的传输问题等价化为奇异的局域边界域积分方程组。研究了相应的局域边界域积分算子的Fredholm性，并在适当的Sobolev-Sloboadeskii(Bessel势)空间中建立了它的可逆性，从而得到了局域边界域积分方程组和相应的声散射传输问题的存在唯一性结果。
We consider the time‐harmonic acoustic wave scattering by a boundedanisotropic inhomogeneityembedded in an unboundedanisotropichomogeneous medium. The material parameters may have discontinuities across the interface between the inhomogeneous interior and homogeneous exterior regions. The corresponding mathematical problem is formulated as a transmission problems for a second‐order elliptic partial differential equation of Helmholtz type with discontinuous variable coefficients. Using a localised quasi‐parametrix based on the harmonic fundamental solution, the transmission problem for arbitrary values of the frequency parameter is reduced equivalently to a system ofsingular localised boundary‐domain integral equations. Fredholm properties of the correspondinglocalised boundary‐domain integral operatorare studied and its invertibility is established in appropriate Sobolev‐Slobodetskii (Bessel potential) spaces, which implies existence and uniqueness results for the localised boundary‐domain integral equations system and the corresponding acoustic scattering transmission problem.