Abstract In this paper, we present some controllability results for linear and nonlinear phase-field systems of Caginalp type considered in a bounded interval of R when the scalar control force acts on the temperature equation of the system by means of the Dirichlet condition on one of the endpoints of the interval. In order to prove the linear result we use the moment method providing an estimate of the cost of fast controls. Using this estimate and following the methodology developed in [19] , we prove a local exact boundary controllability result to constant trajectories of the nonlinear phase-field system. To the authors' knowledge, this is the first nonlinear boundary controllability result in the framework of non-scalar parabolic systems, framework in which some “hyperbolic” behaviors could arise.

中文翻译：

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具有一个控制力的一维相场系统的边界可控性

摘要 在本文中，当标量控制力通过狄利克雷条件作用在系统的温度方程上时，我们给出了在 R 的有界区间内考虑的 Caginalp 型线性和非线性相场系统的一些可控性结果。区间的端点。为了证明线性结果，我们使用矩方法提供快速控制成本的估计。使用此估计并遵循 [19] 中开发的方法，我们证明了非线性相场系统恒定轨迹的局部精确边界可控性结果。据作者所知，这是非标量抛物线系统框架中的第一个非线性边界可控性结果，在该框架中可能会出现一些“双曲线”行为。