This analysis reveals unique solutions to elliptic and parabolic equations on metric graphs, indicating the role of potential and density.
We investigate uniqueness of solutions to certain classes of elliptic and parabolic equations posed on metric graphs. In particular, we address the linear Schr\"odinger equation with a potential, and the heat equation with a variable density. We assume suitable growth conditions on the solutions, which are related to the behaviour at infinity of the potential or of the density.
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Meglioli et al. (2025) studied this question.
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