基于惩罚HUM方法的抛物型方程数值脉冲能控性
Numerical impulse controllability for parabolic equations by a penalized HUM approach
AI总结：
本文通过惩罚HUM结合共轭梯度法，数值计算抛物型方程在不同边界条件下的最小L²范数脉冲控制，并验证了理论能控性结果。
摘要：
本文给出了一项比较研究，用于数值计算具有各种边界条件的抛物型方程的脉冲近似控制。最近，基于Carleman对易子方法，利用单时刻的对数凸性估计，已经研究了理论能控性结果。我们提出了一种数值算法，通过采用惩罚Hilbert唯一性方法（HUM）并结合共轭梯度（CG）方法，来计算具有最小$L^2$-范数的脉冲控制。我们考虑了静态边界条件（Dirichlet和Neumann）以及动态边界条件。基于我们开发的算法，给出了一些数值实验，以验证和比较理论脉冲能控性结果。
英文摘要：
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.
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