| 粗糙曲面上各向异性介质层散射问题的适定性 |
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| 引用本文： | 栾天,马富明.粗糙曲面上各向异性介质层散射问题的适定性[J].吉林大学学报(理学版),2012,50(2):213-218. |
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| 作者姓名： | 栾天 马富明 |
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| 作者单位： | 1. 吉林大学 数学研究所, 长春 130012,2. 北华大学 数学学院, 吉林 吉林 132013 |
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| 基金项目： | 国家自然科学基金(批准号:10971083) |
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| 摘 要： | 考虑时谐声波在无界粗糙声软界面上各项异性介质中散射问题的数学模型, 先将问题转化为变分形式, 验证了双线性形式满足inf sup条件, 通过建立Rellich型恒等式, 并应用广义Lax Milgram定理, 证明了变分问题对任意波数都是唯一可解的, 同时给出了解的先验估计. 所得结果也适合于更一般的介质问题, 不再局限于各项同性介质.
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| 关 键 词： | 散射问题 Helmholtz方程 粗糙曲面 |
| 收稿时间： | 2011-10-01 |
Well-Posedness of Anisotropic Layers Scattering above Rough Surfaces |
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| LUAN Tian,MA Fu-ming.Well-Posedness of Anisotropic Layers Scattering above Rough Surfaces[J].Journal of Jilin University: Sci Ed,2012,50(2):213-218. |
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| Authors: | LUAN Tian MA Fu-ming |
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| Institution: | 1. Institute of Mathematics, Jilin University, Changchun 130012, China;2. College of Mathematics, Beihua University, Jilin 132013, Jilin Province, China |
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| Abstract: | We considered the mathematical model of scattering prob lem for time harmonic acoustic waves in anisotropic media above an unbounded sou nd soft rough surface.We gave a variational form of the problem and established the inf-sup condition of the sesquilinear form.By means of a Rellich-like id entity and the generalized Lax-Milgram theorem,we proved that the variatio nal problem is uniquely solvable for arbitrary wave number and we also gave a pr iori estimation.These results are available for more general media besides isotropic ones. |
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| Keywords: | scattering problem Helmholtz equation rough surface |
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