{"paper":{"title":"Nonexistence Results for Semilinear Parabolic and Hyperbolic Equations on Metric Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.DG"],"primary_cat":"math.AP","authors_text":"Haohang Zhang, Yang Liu, Yong Lin","submitted_at":"2026-06-07T07:23:05Z","abstract_excerpt":"This paper investigates the nonexistence of solutions to semilinear parabolic and hyperbolic inequalities with positive potentials on metric graphs, including both nonnegative solutions and sign-changing solutions. The Laplacian under consideration is of a nonstandard type, incorporating contributions from both the vertices and edges of the metric graph. We construct a new pseudo-metric and introduce suitable space-time test functions of either coupled or separated type. Under suitable weighted space-time volume growth conditions on the potential, we establish nonexistence results for very wea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08490","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08490/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}