We consider a structural-acoustic wall problem in three dimensions, in which the structural wall is modeled by a 2D Kirchhoff-Boussinesq plate and the acoustic medium is subject to boundary damping. For this model we study the existence of a continuous nonlinear semigroup associated with the model in the finite energy space. We show that strong/weak continuity of the semigroups depends on the support of the boundary damping. The complications are related to supercritical nonlinearity exhibited by the plate along with the compromised boundary regularity of the acoustic waves. Compensated compactness methods along with a hidden boundary regularity of hyperbolic traces are exploited in order to establish weak (resp. strong) generation of a nonlinear semigroup subjected to feedback forces placed on the boundary of the acoustic medium.

我们在三个维度上考虑结构-声学墙问题，其中结构墙由二维 Kirchhoff-Boussinesq 板建模，声学介质受边界阻尼影响。对于这个模型，我们研究了在有限能量空间中与模型相关的连续非线性半群的存在。我们表明半群的强/弱连续性取决于边界阻尼的支持。复杂性与板表现出的超临界非线性以及声波边界规则性受损有关。补偿紧致度方法以及双曲线轨迹的隐藏边界规则被利用，以建立受到放置在声介质边界上的反馈力的非线性半群的弱（或强）生成。