{"paper":{"title":"Well-posedness of the initial value problem for the Ostrovsky-Hunter equation with spatially dependent flux","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giuseppe Maria Coclite, Neelabja Chatterjee, Nils Henrik Risebro","submitted_at":"2019-05-22T09:50:10Z","abstract_excerpt":"In this paper we study the Ostrovsky-Hunter equation for the case where the flux function $f(x, u)$ may depend on the spatial variable with certain smoothness. Our main results are that if the flux function is smooth enough (specified later), then there exists a unique entropy solution. To show the existence, after proving some a priori estimates we have used the method of compensated compactness and to prove the uniqueness we have employed the method of doubling of variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09041","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":""},"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"}