We consider the well-posedness of classical boundary value problems in a theory of bending of thin plates which incorporates the effects of surface elasticity via the Gurtin–Murdoch surface model. We employ the fundamental solution of the governing system of equations to develop integral-type solutions of the corresponding Dirichlet, Neumann, and Robin boundary value problems. Using the boundary integral equation method, we subsequently establish results for the existence of a solution in the appropriate function spaces.

中文翻译：

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具有Gurtin–Murdoch表面弹性的薄板弯曲时解的存在性

我们在薄板弯曲理论中考虑了经典边值问题的适定性，该理论通过Gurtin-Murdoch曲面模型结合了表面弹性的影响。我们采用方程式控制系统的基本解来开发相应Dirichlet，Neumann和Robin边值问题的积分型解。使用边界积分方程法，我们随后在适当的函数空间中建立了解的存在性的结果。