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In this paper, we investigate Carleman estimate and its applications for the linear Ginzburg-Landau equation with the complex discontinuous coefficient. We establish the Carleman estimate for the transmission linear Ginzburg-Landau equation. Furthermore, we provide two applications to inverse source problem and observability based on the established Carleman estimate. The first one is to prove the stability of the inverse source problem. The second one is to prove an observability inequality for the backward transmission linear Ginzburg-Landau equation.
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Zhao et al. (2026) studied this question.
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