Abstract In this article, we consider optimal control problems for the one-dimensional Frémond model for shape memory alloys. This model is constructed in terms of basic functionals like free energy and pseudo-potential of dissipation. The state problem is expressed by a system of partial differential equations involving the balance equations for energy and momentum. We prove the existence of an optimal control that minimizes the cost functional for a nonlinear and nonsmooth state problem. Moreover, we show the necessary condition of the optimal pair by using optimal control problems for approximating systems.

中文翻译：

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一维 Frémond 模型形状记忆合金的优化控制

摘要 在本文中，我们考虑了形状记忆合金的一维 Frémond 模型的最优控制问题。该模型是根据自由能和耗散赝势等基本泛函构建的。状态问题由包含能量和动量平衡方程的偏微分方程组表示。我们证明了一个最优控制的存在，它可以最小化非线性和非光滑状态问题的成本函数。此外，我们通过使用逼近系统的最优控制问题来展示最优对的必要条件。