{"id":"https://openalex.org/W3024175766","doi":"https://doi.org/10.3934/nhm.2021020","title":"Reduction of a model for sodium exchanges in kidney nephron","display_name":"Reduction of a model for sodium exchanges in kidney nephron","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3024175766","doi":"https://doi.org/10.3934/nhm.2021020","mag":"3024175766"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2021020","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021020","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/nhm.2021020","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070258886","display_name":"Marta Marulli","orcid":"https://orcid.org/0000-0003-0705-2439"},"institutions":[{"id":"https://openalex.org/I4387154995","display_name":"Math\u00e9matiques Appliqu\u00e9es \u00e0 Paris 5","ror":"https://ror.org/04yrrdj53","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4387154995"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Marta Marulli","raw_affiliation_strings":["MAP5 - UMR 8145, LAGA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MAP5 - UMR 8145, LAGA","institution_ids":["https://openalex.org/I4387154995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076919061","display_name":"Vuk Mili\u0161i\u0107","orcid":"https://orcid.org/0000-0001-5530-2426"},"institutions":[{"id":"https://openalex.org/I4210102686","display_name":"Laboratoire Analyse, G\u00e9om\u00e9trie et Applications","ror":"https://ror.org/018nzqy79","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210102686","https://openalex.org/I4210141950","https://openalex.org/I48825208"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Vuk Mili\u0161i$\\grave{\\rm{c}}$","raw_affiliation_strings":["LAGA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAGA","institution_ids":["https://openalex.org/I4210102686"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055143921","display_name":"Nicolas Vauchelet","orcid":"https://orcid.org/0000-0002-5683-8633"},"institutions":[{"id":"https://openalex.org/I4210102686","display_name":"Laboratoire Analyse, G\u00e9om\u00e9trie et Applications","ror":"https://ror.org/018nzqy79","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210102686","https://openalex.org/I4210141950","https://openalex.org/I48825208"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Vauchelet","raw_affiliation_strings":["LAGA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAGA","institution_ids":["https://openalex.org/I4210102686"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5070258886"],"corresponding_institution_ids":["https://openalex.org/I4387154995"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01779961,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"4","first_page":"609","last_page":"609"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9786999821662903,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9786999821662903,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9742000102996826,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.958899974822998,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nephron","display_name":"Nephron","score":0.846000611782074},{"id":"https://openalex.org/keywords/epithelium","display_name":"Epithelium","score":0.6428560018539429},{"id":"https://openalex.org/keywords/lumen","display_name":"Lumen (anatomy)","score":0.5275530219078064},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5081675052642822},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4587341845035553},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4578174650669098},{"id":"https://openalex.org/keywords/sodium","display_name":"Sodium","score":0.44754424691200256},{"id":"https://openalex.org/keywords/kidney","display_name":"Kidney","score":0.4187380075454712},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.40163829922676086},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3587803244590759},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3530377745628357},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.248214453458786},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.19160300493240356},{"id":"https://openalex.org/keywords/cell-biology","display_name":"Cell biology","score":0.1737508773803711},{"id":"https://openalex.org/keywords/endocrinology","display_name":"Endocrinology","score":0.13375991582870483},{"id":"https://openalex.org/keywords/pathology","display_name":"Pathology","score":0.12008392810821533},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.07868853211402893}],"concepts":[{"id":"https://openalex.org/C2781231759","wikidata":"https://www.wikidata.org/wiki/Q58184","display_name":"Nephron","level":3,"score":0.846000611782074},{"id":"https://openalex.org/C529295009","wikidata":"https://www.wikidata.org/wiki/Q41301","display_name":"Epithelium","level":2,"score":0.6428560018539429},{"id":"https://openalex.org/C131631996","wikidata":"https://www.wikidata.org/wiki/Q1141325","display_name":"Lumen (anatomy)","level":2,"score":0.5275530219078064},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5081675052642822},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4587341845035553},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4578174650669098},{"id":"https://openalex.org/C537181965","wikidata":"https://www.wikidata.org/wiki/Q658","display_name":"Sodium","level":2,"score":0.44754424691200256},{"id":"https://openalex.org/C2780091579","wikidata":"https://www.wikidata.org/wiki/Q9377","display_name":"Kidney","level":2,"score":0.4187380075454712},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.40163829922676086},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3587803244590759},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3530377745628357},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.248214453458786},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.19160300493240356},{"id":"https://openalex.org/C95444343","wikidata":"https://www.wikidata.org/wiki/Q7141","display_name":"Cell biology","level":1,"score":0.1737508773803711},{"id":"https://openalex.org/C134018914","wikidata":"https://www.wikidata.org/wiki/Q162606","display_name":"Endocrinology","level":1,"score":0.13375991582870483},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.12008392810821533},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.07868853211402893},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3934/nhm.2021020","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021020","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2005.07419","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.07419","pdf_url":"https://arxiv.org/pdf/2005.07419","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"text"},{"id":"mag:3024175766","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2005.07419","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-02578120v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02578120","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, 2020, ⟨10.3934/nhm.2021020⟩","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:b1f1a2cedf094d088c821152242f4f74","is_oa":false,"landing_page_url":"https://doaj.org/article/b1f1a2cedf094d088c821152242f4f74","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 16, Iss 4, Pp 609-636 (2021)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2005.07419","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2005.07419","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2021020","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021020","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.4099999964237213,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W196325668","https://openalex.org/W285505819","https://openalex.org/W842313687","https://openalex.org/W1489458628","https://openalex.org/W1512483677","https://openalex.org/W1546846082","https://openalex.org/W1570725637","https://openalex.org/W1571871558","https://openalex.org/W1963875587","https://openalex.org/W1981258689","https://openalex.org/W1981825355","https://openalex.org/W1994412765","https://openalex.org/W2019136397","https://openalex.org/W2040330758","https://openalex.org/W2043196193","https://openalex.org/W2053489483","https://openalex.org/W2064988553","https://openalex.org/W2073447845","https://openalex.org/W2080650843","https://openalex.org/W2244778532","https://openalex.org/W2251490743","https://openalex.org/W2266487441","https://openalex.org/W2461229457","https://openalex.org/W2479687372","https://openalex.org/W2527990943","https://openalex.org/W2561819587","https://openalex.org/W2586499109","https://openalex.org/W2619147374","https://openalex.org/W2788017733","https://openalex.org/W2890949316","https://openalex.org/W2916038186","https://openalex.org/W2962839817","https://openalex.org/W3001662499","https://openalex.org/W4238313514"],"related_works":["https://openalex.org/W3001830462"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>This":[1],"work":[2],"deals":[3],"with":[4,135],"a":[5,12,16,49,58,116,131,189],"mathematical":[6,50],"analysis":[7],"of":[8,15,52,57,105,115,164],"sodium's":[9],"transport":[10],"in":[11],"tubular":[13],"architecture":[14],"kidney":[17],"nephron.":[18],"The":[19,126],"nephron":[20],"is":[21,128],"modelled":[22],"by":[23,86],"two":[24],"counter-current":[25],"tubules.":[26],"Ionic":[27],"exchange":[28],"occurs":[29],"at":[30],"the":[31,34,37,41,44,71,89,106,162,184],"interface":[32],"between":[33,40,91],"tubules":[35],"and":[36,39,43,93,137,158,175,181],"epithelium":[38,42,94],"surrounding":[45],"environment":[46],"(interstitium).":[47],"From":[48],"point":[51],"view,":[53],"this":[54,75],"model":[55],"consists":[56],"5<inline-formula><tex-math":[59,107,171],"id=\"M1\">\\begin{document}$":[60],"\\times":[61,109,120,173,178],"$\\end{document}</tex-math></inline-formula>5":[62,110,174],"semi-linear":[63],"hyperbolic":[64],"system.":[65],"In":[66,74,140],"literature":[67],"similar":[68],"models":[69,82],"neglect":[70],"epithelial":[72,124],"layers.":[73,125],"paper,":[76],"we":[77,145],"show":[78,98,143,182],"rigorously":[79],"that":[80,88,99],"such":[81],"may":[83],"be":[84],"obtained":[85],"assuming":[87],"permeabilities":[90,102],"lumen":[92],"are":[95],"large.":[96],"We":[97,167],"when":[100],"these":[101],"grow,":[103],"solutions":[104],"id=\"M2\">\\begin{document}$":[108],"system":[111,122],"converge":[112],"to":[113,142,154,159],"those":[114],"reduced":[117],"3<inline-formula><tex-math":[118,176],"id=\"M3\">\\begin{document}$":[119],"$\\end{document}</tex-math></inline-formula>3":[121,179],"without":[123],"problem":[127],"defined":[129],"on":[130],"bounded":[132],"spacial":[133],"domain":[134],"initial":[136,156],"boundary":[138],"data.":[139],"order":[141],"convergence,":[144],"use":[146],"<inline-formula><tex-math":[147],"id=\"M4\">\\begin{document}$":[148],"{{{\\rm{BV}}}}":[149],"$\\end{document}</tex-math></inline-formula>":[150],"compactness,":[151],"which":[152],"leads":[153],"introduce":[155],"layers":[157],"handle":[160],"carefully":[161],"presence":[163],"lateral":[165],"boundaries.":[166],"then":[168],"discretize":[169],"both":[170],"id=\"M5\">\\begin{document}$":[172],"id=\"M6\">\\begin{document}$":[177],"systems,":[180],"numerically":[183],"same":[185],"asymptotic":[186],"result,":[187],"for":[188],"fixed":[190],"meshsize.</p>":[191]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}