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

2025/03/26 by Zhu, Xu, Zhou, Wenwen, Wu, Bin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.20628

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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