{"paper":{"title":"Flux-limited solutions for quasi-convex Hamilton-Jacobi equations on networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cyril Imbert (DMA), R Monneau (CERMICS)","submitted_at":"2013-06-11T06:22:45Z","abstract_excerpt":"We study Hamilton-Jacobi equations on networks in the case where Hamiltonians are quasi-convex with respect to the gradient variable and can be discontinuous with respect to the space variable at vertices. First, we prove that imposing a general vertex condition is equivalent to imposing a specific one which only depends on Hamiltonians and an additional free parameter, the flux limiter. Second, a general method for proving comparison principles is introduced. This method consists in constructing a vertex test function to be used in the doubling variable approach. With such a theory and such a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2428","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}