This work presents a comparative study to numerically compute impulse approximate controls for parabolic equations with various boundary conditions. Theoretical controllability results have been recently investigated using a logarithmic convexity estimate at a single time based on a Carleman commutator approach. We propose a numerical algorithm for computing the impulse controls with minimal $L^2$-norms by adapting a penalized Hilbert Uniqueness Method (HUM) combined with a Conjugate Gradient (CG) method. We consider static boundary conditions (Dirichlet and Neumann) and dynamic boundary conditions. Some numerical experiments based on our developed algorithm are given to validate and compare the theoretical impulse controllability results.

翻译：本文提出一种比较研究方法，用于数值计算具有各类边界条件的抛物型方程脉冲近似控制。近期基于卡尔曼交换子方法的单点对数凸性估计，对理论可控性结果进行了探讨。我们通过改进惩罚希尔伯特唯一性方法（HUM）并结合共轭梯度（CG）方法，提出了一种计算具有最小$L^2$范数的脉冲控制的数值算法。研究考虑了静态边界条件（狄利克雷和诺伊曼条件）与动态边界条件。基于所开发算法的数值实验验证并比较了脉冲理论可控性结果。