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arXiv · 2503.20628

Carleman estimate for full-discrete approximations of the complex Ginzburg-Landau equation with dynamic boundary conditions and applications to controllability

Xu Zhu·Wenwen Zhou·Bin Wu
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Abstract

In this paper, we investigate Carleman estimate and controllability result for the fully-discrete approximations of a one-dimensional Ginzburg-Landau equation with dynamic boundary conditions. We first establish a new discrete Carleman estimate for the corresponding adjoint system. Based on this Carleman estimate, we obtain a relaxed observability inequality for the adjoint system, and then a controllability result for the fully-discrete Ginzburg-Landau equation with dynamic boundary conditions.

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Xu Zhu, Wenwen Zhou, Bin Wu. 2025-03-26. Carleman estimate for full-discrete approximations of the complex Ginzburg-Landau equation with dynamic boundary conditions and applications to controllability. https://arxiv.org/abs/2503.20628

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