{"id":"https://openalex.org/W7214401183","doi":"https://doi.org/10.48550/arxiv.2609.29987","title":"A convex numerical scheme for the Evans-Gangbo transport-density system, in one, two, and three dimensions","display_name":"A convex numerical scheme for the Evans-Gangbo transport-density system, in one, two, and three dimensions","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214401183","doi":"https://doi.org/10.48550/arxiv.2609.29987"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.29987","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29987","pdf_url":"https://arxiv.org/pdf/2609.29987","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.29987","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013217696","display_name":"Babacar Mbaye Ndiaye","orcid":"https://orcid.org/0000-0001-9033-9806","observed_orcids":["https://orcid.org/0000-0001-9033-9806"]},"institutions":[{"id":"https://openalex.org/I96840727","display_name":"Cheikh Anta Diop University","ror":"https://ror.org/04je6yw13","country_code":"SN","type":"education","lineage":["https://openalex.org/I96840727"]}],"countries":["SN"],"is_corresponding":false,"raw_author_name":"Ndiaye, Babacar Mbaye","raw_affiliation_strings":["Laboratory of Mathematics of Decision and Numerical Analysis University of Cheikh Anta Diop , Dakar , Senegal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Mathematics of Decision and Numerical Analysis University of Cheikh Anta Diop , Dakar , Senegal","institution_ids":["https://openalex.org/I96840727"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046142528","display_name":"Diaraf Seck","orcid":"https://orcid.org/0000-0003-2865-3727","observed_orcids":["https://orcid.org/0000-0003-2865-3727"]},"institutions":[{"id":"https://openalex.org/I96840727","display_name":"Cheikh Anta Diop University","ror":"https://ror.org/04je6yw13","country_code":"SN","type":"education","lineage":["https://openalex.org/I96840727"]}],"countries":["SN"],"is_corresponding":false,"raw_author_name":"Seck, Diaraf","raw_affiliation_strings":["Laboratory of Mathematics of Decision and Numerical Analysis University of Cheikh Anta Diop , Dakar , Senegal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Mathematics of Decision and Numerical Analysis University of Cheikh Anta Diop , Dakar , Senegal","institution_ids":["https://openalex.org/I96840727"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I96840727"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/optimal-transport","display_name":"optimal transport","score":0.8050000071525574},{"id":"https://openalex.org/keywords/monge-kantorovich-problem","display_name":"Monge-Kantorovich problem","score":0.7820000052452087},{"id":"https://openalex.org/keywords/second-order-cone-programming","display_name":"second-order cone programming","score":0.9200000166893005},{"id":"https://openalex.org/keywords/kantorovich-potential","display_name":"Kantorovich potential","score":0.843999981880188},{"id":"https://openalex.org/keywords/transport-maps","display_name":"transport maps","score":0.5860000252723694},{"id":"https://openalex.org/keywords/mass-conservation","display_name":"mass conservation","score":0.593999981880188},{"id":"https://openalex.org/keywords/strong-duality","display_name":"strong duality","score":0.8090000152587891},{"id":"https://openalex.org/keywords/three-dimensional-transport","display_name":"three-dimensional transport","score":0.5170000195503235}],"concepts":[{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6675000190734863},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5827999711036682},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.49810001254081726},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4909000098705292},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.43880000710487366},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.43869999051094055},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4189000129699707},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.41850000619888306},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.398499995470047},{"id":"https://openalex.org/C2989209122","wikidata":"https://www.wikidata.org/wiki/Q178512","display_name":"Mass transport","level":2,"score":0.39469999074935913},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.39169999957084656},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.38929998874664307},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.38920000195503235},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.38260000944137573},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35910001397132874},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.35839998722076416},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3402000069618225},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.31139999628067017},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2930000126361847},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2874000072479248},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27300000190734863},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.2644999921321869},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2581999897956848},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.29987","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29987","pdf_url":"https://arxiv.org/pdf/2609.29987","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.29987","doi":"https://doi.org/10.48550/arxiv.2609.29987","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.29987","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.29987","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29987","pdf_url":"https://arxiv.org/pdf/2609.29987","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214401183.pdf","grobid_xml":"https://content.openalex.org/works/W7214401183.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2785169672","https://openalex.org/W2963956318","https://openalex.org/W3118245667","https://openalex.org/W4297822839","https://openalex.org/W7161939507"],"related_works":["https://openalex.org/W4392939058","https://openalex.org/W2310844257","https://openalex.org/W4213394773","https://openalex.org/W7160604659","https://openalex.org/W7097399133","https://openalex.org/W2056709476","https://openalex.org/W7214304505","https://openalex.org/W2288897864","https://openalex.org/W2074958884","https://openalex.org/W7095813131"],"abstract_inverted_index":{"We":[0,123],"give":[1],"a":[2,22,45,58,67,78,98,108,142,146],"constructive":[3],"numerical":[4],"treatment":[5],"of":[6,148,167],"Monge's":[7],"optimal":[8],"transport":[9,156],"problem":[10,62],"in":[11,51],"1D,":[12],"2D,":[13],"3D,":[14],"following":[15],"Evans-Gangbo:":[16],"the":[17,72,130,138,149,155,164],"map":[18,73],"is":[19],"built":[20],"from":[21],"Kantorovich":[23],"potential":[24],"$u$":[25],"and":[26,94,101,117,136],"density":[27,85],"$a$":[28],"solving":[29],"$-\\mathrm{div}(a\\nabla":[30],"u)":[31],"=":[32,37],"f^+-f^-$,":[33],"via":[34,57],"$\\dot":[35],"T":[36],"-a\\nabla":[38],"u(T)/[(1-t)f^+(T)+tf^-(T)]$,":[39],"$T(0,x)=x$.":[40],"In":[41,48],"1D":[42,80],"this":[43,168],"gives":[44],"closed":[46],"form.":[47],"2D--left":[49],"unfinished":[50],"an":[52],"earlier":[53],"report--we":[54],"obtain":[55],"$(u,a)$":[56],"convex":[59],"Beckmann":[60],"flow":[61],"(second-order-cone":[63],"programming),":[64],"cross-checked":[65],"against":[66],"dual":[68],"LP,":[69],"then":[70],"build":[71],"by":[74,111],"direct":[75],"integration":[76],"or":[77],"ray-based":[79],"\"clock\"":[81],"ODE":[82],"with":[83],"explicit":[84],"per":[86],"ray.":[87],"Validation":[88],"uses":[89],"strong":[90],"duality,":[91],"mass":[92,116],"conservation,":[93],"vanishing-regularization":[95],"limits,":[96],"on":[97,141,163],"translation-invariant":[99],"case":[100],"two":[102],"2D":[103,131,150],"examples":[104],"(a":[105],"radial":[106,143],"cone,":[107],"checkerboard)":[109],"checked":[110],"symmetry;":[112],"both":[113],"show":[114],"boundary-concentrated":[115],"non-unique":[118],"flux":[119],"where":[120],"supports":[121],"touch.":[122],"extend":[124],"to":[125,133],"3D":[126],"(theory":[127],"unchanged),":[128],"matching":[129],"answer":[132],"six":[134],"digits":[135],"reproducing":[137],"same":[139],"phenomena":[140],"ball,":[144],"exposing":[145],"limit":[147],"visualization":[151],"style.":[152],"Movies":[153],"illustrating":[154],"maps":[157],"are":[158],"available":[159],"as":[160],"ancillary":[161],"files":[162],"arXiv":[165],"page":[166],"submission.":[169]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-26T00:00:00"}