{"id":"https://openalex.org/W2049324412","doi":"https://doi.org/10.1137/s0036139993249524","title":"Analysis of a Conservation PDE With Discontinuous Flux: A Model of Settler","display_name":"Analysis of a Conservation PDE With Discontinuous Flux: A Model of Settler","publication_year":1994,"publication_date":"1994-08-01","ids":{"openalex":"https://openalex.org/W2049324412","doi":"https://doi.org/10.1137/s0036139993249524","mag":"2049324412"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139993249524","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139993249524","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032878617","display_name":"Jean\u2010Philippe Chancelier","orcid":"https://orcid.org/0000-0002-0658-2035"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J.-Ph. Chancelier","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081410364","display_name":"Michel Cohen de Lara","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Cohen De Lara","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109102085","display_name":"Frank Pacard","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. Pacard","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5032878617"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1075,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.93220339,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"54","issue":"4","first_page":"954","last_page":"995"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10894","display_name":"Groundwater flow and contamination studies","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10894","display_name":"Groundwater flow and contamination studies","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10564","display_name":"Wastewater Treatment and Nitrogen Removal","score":0.9660000205039978,"subfield":{"id":"https://openalex.org/subfields/2310","display_name":"Pollution"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11188","display_name":"Coagulation and Flocculation Studies","score":0.9168999791145325,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.7380251288414001},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.7076900601387024},{"id":"https://openalex.org/keywords/blanket","display_name":"Blanket","score":0.673119068145752},{"id":"https://openalex.org/keywords/settling","display_name":"Settling","score":0.6196290850639343},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5309618711471558},{"id":"https://openalex.org/keywords/flux","display_name":"Flux (metallurgy)","score":0.5081954002380371},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4726511538028717},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4559207558631897},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4486442506313324},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.42202746868133545},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34531503915786743},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29542165994644165},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.24941691756248474},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.20013034343719482},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.13338801264762878},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13234812021255493}],"concepts":[{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.7380251288414001},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.7076900601387024},{"id":"https://openalex.org/C2779261148","wikidata":"https://www.wikidata.org/wiki/Q5852","display_name":"Blanket","level":2,"score":0.673119068145752},{"id":"https://openalex.org/C173209714","wikidata":"https://www.wikidata.org/wiki/Q923906","display_name":"Settling","level":2,"score":0.6196290850639343},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5309618711471558},{"id":"https://openalex.org/C68709404","wikidata":"https://www.wikidata.org/wiki/Q1134475","display_name":"Flux (metallurgy)","level":2,"score":0.5081954002380371},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4726511538028717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4559207558631897},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4486442506313324},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.42202746868133545},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34531503915786743},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29542165994644165},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.24941691756248474},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.20013034343719482},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.13338801264762878},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13234812021255493},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139993249524","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139993249524","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Clean water and sanitation","score":0.8600000143051147,"id":"https://metadata.un.org/sdg/6"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W27085871","https://openalex.org/W1508316952","https://openalex.org/W1588149815","https://openalex.org/W1603673253","https://openalex.org/W1608590953","https://openalex.org/W1850134083","https://openalex.org/W1969631053","https://openalex.org/W1992812527","https://openalex.org/W2038991247","https://openalex.org/W2062062852","https://openalex.org/W2088350404","https://openalex.org/W4213087550","https://openalex.org/W4231851426"],"related_works":["https://openalex.org/W2388844564","https://openalex.org/W2044778064","https://openalex.org/W4200539879","https://openalex.org/W2942060259","https://openalex.org/W2954773362","https://openalex.org/W2804435182","https://openalex.org/W2392411846","https://openalex.org/W3143691993","https://openalex.org/W2177300204","https://openalex.org/W4254441412"],"abstract_inverted_index":{"A":[0,89],"dynamic":[1],"model":[2,90],"of":[3,11,62,69,76,94,119,122,128],"the":[4,8,33,40,60,67,70,74,104,111,114,120,133],"settling":[5],"process":[6],"in":[7,96,126],"secondary":[9],"settler":[10],"a":[12,19,77,123],"wastewater":[13],"treatment":[14],"plant":[15,134],"is":[16,98],"given":[17],"by":[18],"nonlinear":[20],"scalar":[21],"conservation":[22],"law":[23],"$c_t":[24],"+":[25],"\\psi":[26],"(":[27,43],"x,c":[28,44],")_x":[29],"=":[30],"0$":[31],"for":[32],"sludge":[34,78,124],"concentration":[35],"$c(":[36],"t,x":[37],")$,":[38],"where":[39],"flux":[41],"function$\\psi":[42],")$":[45],"presents":[46],"discontinuities.":[47],"The":[48],"authors":[49],"analyze":[50],"this":[51],"partial":[52],"differential":[53],"equation":[54],"(PDE)":[55],"with":[56,86,91,113],"emphasis":[57],"both":[58],"on":[59,66],"existence":[61],"stationary":[63],"solutions":[64],"and":[65,81],"evolution":[68],"shock":[71],"corresponding":[72],"to":[73,100,109,132],"rising":[75,121],"blanket.":[79],"Theoretical":[80],"numerical":[82],"simulations":[83],"are":[84,135],"compared":[85],"real":[87],"data.":[88,115],"two":[92],"classes":[93],"particles":[95],"interaction":[97],"introduced":[99],"take":[101],"into":[102],"account":[103],"thickening":[105],"process,":[106],"which":[107],"appears":[108],"improve":[110],"fit":[112],"Furthermore,":[116],"regulation":[117],"strategies":[118],"blanket":[125],"case":[127],"important":[129],"water":[130],"admission":[131],"proposed.":[136]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
