{"id":"https://openalex.org/W2067680596","doi":"https://doi.org/10.1137/050640321","title":"Global Weak Solutions to Equations of Compressible Miscible Flows in Porous Media","display_name":"Global Weak Solutions to Equations of Compressible Miscible Flows in Porous Media","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2067680596","doi":"https://doi.org/10.1137/050640321","mag":"2067680596"},"language":"en","primary_location":{"id":"doi:10.1137/050640321","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050640321","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5029357513","display_name":"Youcef Amirat","orcid":"https://orcid.org/0000-0002-5357-7968"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Y. Amirat","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044537694","display_name":"V. V. Shelukhin","orcid":"https://orcid.org/0000-0002-0058-1226"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V. Shelukhin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5029357513"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7962,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.82875918,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"38","issue":"6","first_page":"1825","last_page":"1846"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.7684999704360962,"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":0.7684999704360962,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.05739999935030937,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.03280000016093254,"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/mathematics","display_name":"Mathematics","score":0.7316656112670898},{"id":"https://openalex.org/keywords/lagrangian-and-eulerian-specification-of-the-flow-field","display_name":"Lagrangian and Eulerian specification of the flow field","score":0.7315366268157959},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.7132982015609741},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6088695526123047},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5868091583251953},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5255305171012878},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.5106647610664368},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5042589902877808},{"id":"https://openalex.org/keywords/compressible-flow","display_name":"Compressible flow","score":0.4641284942626953},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4627283811569214},{"id":"https://openalex.org/keywords/second-derivative","display_name":"Second derivative","score":0.4414105713367462},{"id":"https://openalex.org/keywords/weak-solution","display_name":"Weak solution","score":0.42236340045928955},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.3722382187843323},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.25541529059410095},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.19474291801452637},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17132017016410828},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.10644343495368958}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7316656112670898},{"id":"https://openalex.org/C89901390","wikidata":"https://www.wikidata.org/wiki/Q6418927","display_name":"Lagrangian and Eulerian specification of the flow field","level":4,"score":0.7315366268157959},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.7132982015609741},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6088695526123047},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5868091583251953},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5255305171012878},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.5106647610664368},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5042589902877808},{"id":"https://openalex.org/C5192115","wikidata":"https://www.wikidata.org/wiki/Q2705141","display_name":"Compressible flow","level":3,"score":0.4641284942626953},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4627283811569214},{"id":"https://openalex.org/C33257320","wikidata":"https://www.wikidata.org/wiki/Q1932744","display_name":"Second derivative","level":2,"score":0.4414105713367462},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.42236340045928955},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.3722382187843323},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.25541529059410095},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.19474291801452637},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17132017016410828},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.10644343495368958},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050640321","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050640321","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00477034v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00477034","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, 2007, 38 (6), pp.1825-1846","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1965012454","https://openalex.org/W1972395226","https://openalex.org/W1981875677","https://openalex.org/W2006096941","https://openalex.org/W2008683313","https://openalex.org/W2057579751","https://openalex.org/W2081431069","https://openalex.org/W2132627385","https://openalex.org/W2330325083"],"related_works":["https://openalex.org/W2046564732","https://openalex.org/W331924088","https://openalex.org/W2952025544","https://openalex.org/W2280943523","https://openalex.org/W1971894549","https://openalex.org/W1847914272","https://openalex.org/W2340295003","https://openalex.org/W2067955258","https://openalex.org/W2008188920","https://openalex.org/W2042746256"],"abstract_inverted_index":{"We":[0,59],"study":[1],"the":[2,26,31,43,50,55,71],"one\u2010dimensional":[3],"equations":[4,17,35],"governing":[5],"compressible":[6],"flows":[7],"of":[8,36,64],"m":[9],"miscible":[10],"components":[11],"in":[12,70],"a":[13,21],"porous":[14],"medium.":[15],"The":[16,34],"are":[18,39],"reduced":[19],"to":[20],"quasi\u2010linear":[22],"parabolic":[23,44],"system":[24,38],"for":[25,46],"discharge":[27],"function":[28],"P":[29],"and":[30,54,73],"concentrations":[32],"$c_i$.":[33],"this":[37],"strongly":[40],"coupled":[41],"since":[42],"equation":[45],"$c_i$":[47],"contains":[48],"both":[49,69],"second":[51,56],"derivative":[52,57],"$c_{ixx}$":[53],"$P_{xx}$.":[58],"prove":[60],"global":[61],"weak":[62],"solvability":[63],"an":[65],"initial":[66],"boundary\u2010value":[67],"problem":[68],"Eulerian":[72],"Lagrangian":[74],"formulations.":[75]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
