{"paper":{"title":"On scalar nonlinear balance laws with singular nonlocal sources","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Scalar nonlinear balance laws with singular nonlocal sources admit global entropy weak solutions in L2 under convexity and kernel conditions.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Evangelia Ftaka, Khai T. Nguyen","submitted_at":"2026-05-17T12:37:06Z","abstract_excerpt":"We investigate one-dimensional scalar balance laws with singular convolution-type source terms. Under appropriate convexity and kernel assumptions, we establish the global existence of entropy weak solutions in ${\\bf L}^2(\\mathbb{R})$, together with two partial uniqueness results, in the ${\\bf L}^2$-periodic setting and non-periodic setting with ${\\bf L}^1(\\mathbb{R})$ kernel. In the ${\\bf L}^1$-kernel case, the characteristic speed satisfies an Oleinik-type estimate, and entropy weak solutions possess locally bounded fractional variation for all positive times. Furthermore, we derive a simple"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under appropriate convexity and kernel assumptions, we establish the global existence of entropy weak solutions in L²(ℝ), together with two partial uniqueness results, in the L²-periodic setting and non-periodic setting with L¹(ℝ) kernel.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The convexity assumptions on the flux function and the specific regularity or positivity conditions imposed on the singular kernel (invoked in the abstract to obtain global existence and the Oleinik-type estimate).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Global existence of entropy weak solutions and partial uniqueness are established for scalar balance laws with singular nonlocal sources, plus an Oleinik-type estimate and a local smoothness/wave-breaking criterion.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Scalar nonlinear balance laws with singular nonlocal sources admit global entropy weak solutions in L2 under convexity and kernel conditions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"c8083b1a8e2c2a08065420f07dd95897566c8856bff578b032bd1f78a849fc5b"},"source":{"id":"2605.17422","kind":"arxiv","version":1},"verdict":{"id":"5a54013e-ac93-4149-83e2-e597f0de09be","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:42:40.609351Z","strongest_claim":"Under appropriate convexity and kernel assumptions, we establish the global existence of entropy weak solutions in L²(ℝ), together with two partial uniqueness results, in the L²-periodic setting and non-periodic setting with L¹(ℝ) kernel.","one_line_summary":"Global existence of entropy weak solutions and partial uniqueness are established for scalar balance laws with singular nonlocal sources, plus an Oleinik-type estimate and a local smoothness/wave-breaking criterion.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The convexity assumptions on the flux function and the specific regularity or positivity conditions imposed on the singular kernel (invoked in the abstract to obtain global existence and the Oleinik-type estimate).","pith_extraction_headline":"Scalar nonlinear balance laws with singular nonlocal sources admit global entropy weak solutions in L2 under convexity and kernel conditions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17422/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.617525Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:52:12.461596Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.737083Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.683166Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"c108489524d83b427cb14f8af4c42b90300d1830407d537b6bc7905e99fe948e"},"references":{"count":27,"sample":[{"doi":"","year":2012,"title":"F. Ancona, O. Glass, K. T. Nguyen, Lower compactness estimates for scalar balance laws,Comm. Pure Appl. Math.65(2012), 1303-1329–336","work_id":"54168848-48bd-49fe-8de7-427b1376a9a7","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"J. Biello and J. K. Hunter, Nonlinear Hamiltonian waves with constant frequency and surface waves on vorticity discontinuities,Comm. Pure Appl. Math.63(2009), 303–336","work_id":"665854f4-e3ae-432c-b5c6-9747203ab289","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"L. Bociu, E. Ftaka, K. T. Nguyen, J. Schino, Piecewise regular solutions to scalar balance laws with singular source terms,Journal of Differential Equations,409(2024), 181–222","work_id":"c0d8b5ab-57e8-478c-9d45-0abf5d0a7c4e","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2000,"title":"Bressan,Hyperbolic Systems of Conservation Laws","work_id":"b1859e54-1db6-45fe-9080-de486f5bf0bc","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"A. Bressan and K. T. Nguyen, Global existence of weak solutions for the Burgers-Hilbert equation.SIAM Journal on Mathematical Analysis.46(2014), 2884–2904","work_id":"2f0a36b5-aa0b-4f1b-9371-584d1b1652d5","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":27,"snapshot_sha256":"0a11c7cc4b0159512c12b7f46ec479e9d77b7b74e725effe094aeac602fa3b3d","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"e1d0ba94220f5744c7a5461e11ec01c567a4551c7f2a2dc8409c97d0425ce0f7"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}