SIAM Journal on Applied Mathematics, Volume 80, Issue 3, Page 1546-1566, January 2020.
We address scattering problems for impenetrable obstacles in an infinite elastic Kirchhoff--Love two-dimensional plate. The analysis is restricted to the purely bending case and the time-harmonic regime. Considering four types of boundary conditions on the obstacle, well-posedness for those problems is proved with the help of a variational approach: (i) for any wave number $k$ when the plate is clamped, simply supported, or roller supported; (ii) for any $k$ except a discrete set when the plate is free (this set is finite for convex obstacles).

中文翻译：

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Kirchhoff-Love无限板中散射问题的适定性

SIAM应用数学杂志，第80卷，第3期，第1546-1566页，2020年1月。
我们解决了无限弹性Kirchhoff-Love二维板中难以穿透的障碍物的散射问题。分析仅限于纯弯曲情况和时谐机制。考虑障碍物上的四种边界条件，借助变分方法证明了这些问题的适定性：（i）对于夹板，简单支撑或辊支撑的任何波数$ k $；（ii）对于任何$ k $，除了板自由时的离散集（此集对于凸障碍物是有限的）。