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Uniqueness of solutions to elliptic and parabolic equations on metric graphs
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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.
Forward citations
Cited by 2 Pith papers
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Rigidity for the heat equation with density on Riemannian manifolds through a conformal change
Uniqueness of zero solutions to the density heat equation on non-compact weighted manifolds is established in weighted L^p spaces, with model-manifold examples showing the density decay conditions are optimal.
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Nonexistence results for the semilinear wave equation on graphs
On infinite weighted graphs, if the graph Laplacian of the distance grows slowly and suitable weighted volume growth holds, every very weak solution of the semilinear wave inequality is identically zero.
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