Abstract We consider a contact model with power-law friction in the antiplane context. Our study focuses on the boundary optimal control, paying special attention to optimality conditions and computational methods. Depending on the exponent of the power-law friction, we are able to deduce an optimality condition for the original problem or for a regularized version of it. Furthermore, we introduce and analyze a computational technique based on linearization, saddle point theory and a fixed point method. For a slightly modified optimal control problem, some numerical experiments are presented.

中文翻译：

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具有幂律摩擦的反平面接触问题的边界优化控制

摘要 我们考虑在反平面环境中具有幂律摩擦的接触模型。我们的研究侧重于边界最优控制，特别关注最优条件和计算方法。根据幂律摩擦的指数，我们能够推导出原始问题或其正则化版本的最优条件。此外，我们介绍并分析了基于线性化、鞍点理论和不动点方法的计算技术。对于稍微修改的最优控制问题，给出了一些数值实验。