{"id":"https://openalex.org/W4288345646","doi":"https://doi.org/10.1007/s00332-023-09896-z","title":"Mathematical Theory of Nonlinear Single-Phase Poroelasticity","display_name":"Mathematical Theory of Nonlinear Single-Phase Poroelasticity","publication_year":2023,"publication_date":"2023-03-10","ids":{"openalex":"https://openalex.org/W4288345646","doi":"https://doi.org/10.1007/s00332-023-09896-z"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-023-09896-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-023-09896-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-023-09896-z.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00332-023-09896-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003203502","display_name":"C.J. van Duijn","orcid":"https://orcid.org/0000-0002-1775-519X"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"education","lineage":["https://openalex.org/I193662353"]},{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"C. J. van Duijn","raw_affiliation_strings":["Department of Earth Sciences, Utrecht University, Utrecht, The Netherlands","Department of Mechanical Engineering, Darcy Center, Eindhoven University of Technology, Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Earth Sciences, Utrecht University, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Darcy Center, Eindhoven University of Technology, Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077009185","display_name":"Andro Mikeli\u0107","orcid":"https://orcid.org/0000-0002-4752-8705"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Andro Mikeli\u0107","raw_affiliation_strings":["Univ Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622, Villeurbanne cedex, France"],"affiliations":[{"raw_affiliation_string":"Univ Lyon, Universit\u00e9 Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622, Villeurbanne cedex, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I4210104796","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003203502"],"corresponding_institution_ids":["https://openalex.org/I193662353","https://openalex.org/I83019370"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.5784,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.79883271,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"33","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10635","display_name":"Hydraulic Fracturing and Reservoir Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10635","display_name":"Hydraulic Fracturing and Reservoir Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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":0.9995999932289124,"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/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/poromechanics","display_name":"Poromechanics","score":0.7380422949790955},{"id":"https://openalex.org/keywords/biot-number","display_name":"Biot number","score":0.6646831631660461},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6645092964172363},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.6584025025367737},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6354405283927917},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.5593772530555725},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5554361343383789},{"id":"https://openalex.org/keywords/mixture-theory","display_name":"Mixture theory","score":0.5470465421676636},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5398181676864624},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.5237871408462524},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.47543099522590637},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.3685382008552551},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19252753257751465},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.1551651954650879},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1510045826435089},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13312721252441406}],"concepts":[{"id":"https://openalex.org/C181965411","wikidata":"https://www.wikidata.org/wiki/Q2314330","display_name":"Poromechanics","level":4,"score":0.7380422949790955},{"id":"https://openalex.org/C115341296","wikidata":"https://www.wikidata.org/wiki/Q864844","display_name":"Biot number","level":2,"score":0.6646831631660461},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6645092964172363},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.6584025025367737},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6354405283927917},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.5593772530555725},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5554361343383789},{"id":"https://openalex.org/C2779736610","wikidata":"https://www.wikidata.org/wiki/Q6884140","display_name":"Mixture theory","level":3,"score":0.5470465421676636},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5398181676864624},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.5237871408462524},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.47543099522590637},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.3685382008552551},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19252753257751465},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.1551651954650879},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1510045826435089},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13312721252441406},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00332-023-09896-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-023-09896-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-023-09896-z.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02144933v1","is_oa":true,"landing_page_url":"https://univ-lyon1.hal.science/hal-02144933","pdf_url":"https://univ-lyon1.hal.science/hal-02144933/document","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":"Journal of Nonlinear Science, 2023, 33 (44), ⟨10.1007/s00332-023-09896-z⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1007/s00332-023-09896-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-023-09896-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-023-09896-z.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8700000047683716,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G209428366","display_name":null,"funder_award_id":"LABEX MILYON (ANR-10-LABX-0070)","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2726473892","display_name":null,"funder_award_id":"ANR-11-IDEX-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2797261717","display_name":null,"funder_award_id":"ANR-19-CU05-032","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3335229504","display_name":null,"funder_award_id":"Avenir","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3584739849","display_name":null,"funder_award_id":"ANR-10-LABX-0070","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4866930200","display_name":null,"funder_award_id":"ANR-11-IDEX","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5122439844","display_name":null,"funder_award_id":"ANR-11-IDEX-0007)","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5549440890","display_name":null,"funder_award_id":"ANR-10-LAB","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5701317573","display_name":null,"funder_award_id":"11-IDEX-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6494969328","display_name":null,"funder_award_id":"ANR-10-LABX-0070","funder_id":"https://openalex.org/F4320326804","funder_display_name":"Universit\u00e9 de Lyon"},{"id":"https://openalex.org/G7211054625","display_name":null,"funder_award_id":"ANR-11-IDEX-0007","funder_id":"https://openalex.org/F4320326804","funder_display_name":"Universit\u00e9 de Lyon"},{"id":"https://openalex.org/G7240651115","display_name":null,"funder_award_id":"ANR-10","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7823808512","display_name":null,"funder_award_id":"ANR-11-IDEX-000","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8318455765","display_name":null,"funder_award_id":"ANR-19","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8339676720","display_name":null,"funder_award_id":"LABEX MILYON (ANR-10-LABX-0070)","funder_id":"https://openalex.org/F4320326804","funder_display_name":"Universit\u00e9 de Lyon"},{"id":"https://openalex.org/G8917127843","display_name":null,"funder_award_id":"LABEX","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320325866","display_name":"Universiteit Hasselt","ror":"https://ror.org/04nbhqj75"},{"id":"https://openalex.org/F4320326804","display_name":"Universit\u00e9 de Lyon","ror":"https://ror.org/01rk35k63"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4288345646.pdf"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W236289633","https://openalex.org/W1516132534","https://openalex.org/W1542994047","https://openalex.org/W1547403762","https://openalex.org/W1969924033","https://openalex.org/W1977727715","https://openalex.org/W1979034594","https://openalex.org/W1982242723","https://openalex.org/W1996541583","https://openalex.org/W2013148915","https://openalex.org/W2013535587","https://openalex.org/W2014562635","https://openalex.org/W2027046172","https://openalex.org/W2075954740","https://openalex.org/W2076330525","https://openalex.org/W2082688453","https://openalex.org/W2085692863","https://openalex.org/W2100203796","https://openalex.org/W2101956120","https://openalex.org/W2119832723","https://openalex.org/W2166079767","https://openalex.org/W2166701390","https://openalex.org/W2199543805","https://openalex.org/W2472843403","https://openalex.org/W2485912565","https://openalex.org/W2734991210","https://openalex.org/W2801862097","https://openalex.org/W2897213722","https://openalex.org/W2963482919","https://openalex.org/W3102060339","https://openalex.org/W4211160782","https://openalex.org/W4246420244","https://openalex.org/W4301454416"],"related_works":["https://openalex.org/W4390465241","https://openalex.org/W2059677665","https://openalex.org/W2735211706","https://openalex.org/W2894257416","https://openalex.org/W57719583","https://openalex.org/W1976747621","https://openalex.org/W2808572609","https://openalex.org/W3097552840","https://openalex.org/W4253934351","https://openalex.org/W2087488124"],"abstract_inverted_index":{"Abstract":[0],"In":[1,57,119],"this":[2],"paper,":[3],"we":[4,60,76,96,136],"study":[5],"the":[6,17,31,34,38,45,48,55,62,70,93,116,120,127,130,138,143,146],"equations":[7],"of":[8,21,33,40,47,54,79,85,155],"nonlinear":[9,94],"poroelasticity":[10],"derived":[11],"from":[12,30,37],"mixture":[13],"theory.":[14],"They":[15],"describe":[16],"quasi-static":[18,63],"mechanical":[19],"behavior":[20],"a":[22,80,98,156],"fluid":[23,35,128],"saturated":[24],"porous":[25],"medium.":[26],"The":[27],"nonlinearity":[28],"arises":[29],"compressibility":[32],"and":[36,42,67,129],"dependence":[39],"porosity":[41],"permeability":[43],"on":[44],"divergence":[46],"displacement.":[49],"We":[50],"point":[51],"some":[52],"limitations":[53],"model.":[56],"our":[58],"approach,":[59],"discretize":[61],"formulation":[64],"in":[65,142],"time":[66,117,140,147],"first":[68],"consider":[69,137],"corresponding":[71],"incremental":[72],"problem.":[73],"For":[74],"this,":[75],"prove":[77],"existence":[78,154],"solution":[81],"using":[82],"Br\u00e9zis\u2019":[83],"theory":[84],"pseudo-monotone":[86],"operators.":[87],"Generalizing":[88],"Biot\u2019s":[89],"free":[90,158],"energy":[91,159],"to":[92,107,115,150],"setting,":[95],"construct":[97,108],"Lyapunov":[99],"functional,":[100],"yielding":[101],"global":[102],"stability.":[103],"This":[104,152],"allows":[105],"us":[106],"bounds":[109],"that":[110],"are":[111,132],"uniform":[112],"with":[113],"respect":[114],"step.":[118],"case":[121,141],"when":[122,145],"dissipative":[123],"interface":[124],"effects":[125],"between":[126],"solid":[131],"taken":[133],"into":[134],"account,":[135],"continuous":[139],"limit":[144],"step":[148],"tends":[149],"zero.":[151],"yields":[153],"weak":[157],"solution.":[160]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}