{"id":"https://openalex.org/W2906801581","doi":"https://doi.org/10.1016/s1874-5717(06)80009-5","title":"Evolution of Rate-Independent Systems","display_name":"Evolution of Rate-Independent Systems","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2906801581","doi":"https://doi.org/10.1016/s1874-5717(06)80009-5","mag":"2906801581"},"language":"en","primary_location":{"id":"doi:10.1016/s1874-5717(06)80009-5","doi":"https://doi.org/10.1016/s1874-5717(06)80009-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s1874-5717(06)80009-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210207239","display_name":"Handbook of differential equations. Evolutionary equations","issn_l":"1874-5717","issn":["1874-5717","2452-0845"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Handbook of Differential Equations: Evolutionary Equations","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W4249155891","display_name":"Handbook of Differential Equations Evolutionary Equations"},"type":"book-chapter","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/A5052253534","display_name":"Alexander Mielke","orcid":"https://orcid.org/0000-0002-4583-3888","observed_orcids":["https://orcid.org/0000-0002-4583-3888"]},"institutions":[{"id":"https://openalex.org/I39343248","display_name":"Humboldt-Universit\u00e4t zu Berlin","ror":"https://ror.org/01hcx6992","country_code":"DE","type":"education","lineage":["https://openalex.org/I39343248"]},{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Alexander Mielke","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Humboldt-Universit\u00e4t zu Berlin, Rudower Chaussee 25, 12489 Berlin (Adlershof), Germany","Weierstra\u03b2-Institut f\u00fcr Angewandte Analysis und Stochastik, Mohrenstra\u03b2e 39, 10117 Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Humboldt-Universit\u00e4t zu Berlin, Rudower Chaussee 25, 12489 Berlin (Adlershof), Germany","institution_ids":["https://openalex.org/I39343248"]},{"raw_affiliation_string":"Weierstra\u03b2-Institut f\u00fcr Angewandte Analysis und Stochastik, Mohrenstra\u03b2e 39, 10117 Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052253534"],"corresponding_institution_ids":["https://openalex.org/I39343248","https://openalex.org/I4210092021"],"apc_list":null,"apc_paid":null,"fwci":38.4425,"has_fulltext":false,"cited_by_count":350,"citation_normalized_percentile":{"value":0.9982906,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"461","last_page":"559"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.6068999767303467,"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"}},"topics":[{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.6068999767303467,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.13670000433921814,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T13261","display_name":"Elasticity and Wave Propagation","score":0.03779999911785126,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/rate-independent-systems","display_name":"rate-independent systems","score":0.996999979019165},{"id":"https://openalex.org/keywords/hysteresis-operators","display_name":"hysteresis operators","score":0.9950000047683716},{"id":"https://openalex.org/keywords/continuum-mechanics","display_name":"continuum mechanics","score":0.8119999766349792},{"id":"https://openalex.org/keywords/limit-problem","display_name":"limit problem","score":0.7350000143051147},{"id":"https://openalex.org/keywords/evolution-equations","display_name":"evolution equations","score":0.5249999761581421}],"concepts":[{"id":"https://openalex.org/C4708273","wikidata":"https://www.wikidata.org/wiki/Q900222","display_name":"Quasistatic process","level":2,"score":0.9183403253555298},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6394271850585938},{"id":"https://openalex.org/C173386949","wikidata":"https://www.wikidata.org/wiki/Q192735","display_name":"Inertial frame of reference","level":2,"score":0.5403940677642822},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4732300043106079},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4249183237552643},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.4245692491531372},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4194275736808777},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3596886992454529},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3514190912246704},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.32406723499298096},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2511737048625946},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.09567767381668091},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s1874-5717(06)80009-5","doi":"https://doi.org/10.1016/s1874-5717(06)80009-5","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s1874-5717(06)80009-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210207239","display_name":"Handbook of differential equations. Evolutionary equations","issn_l":"1874-5717","issn":["1874-5717","2452-0845"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Handbook of Differential Equations: Evolutionary Equations","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":138,"referenced_works":["https://openalex.org/W2370431","https://openalex.org/W3732449","https://openalex.org/W56295171","https://openalex.org/W68540026","https://openalex.org/W107066676","https://openalex.org/W114339823","https://openalex.org/W141106104","https://openalex.org/W155401011","https://openalex.org/W173960919","https://openalex.org/W316812300","https://openalex.org/W331534545","https://openalex.org/W588153840","https://openalex.org/W595325313","https://openalex.org/W638757554","https://openalex.org/W842603002","https://openalex.org/W1500144285","https://openalex.org/W1504430697","https://openalex.org/W1510691963","https://openalex.org/W1518297095","https://openalex.org/W1531962324","https://openalex.org/W1537639429","https://openalex.org/W1547403762","https://openalex.org/W1571840955","https://openalex.org/W1577624779","https://openalex.org/W1582617215","https://openalex.org/W1584006925","https://openalex.org/W1595744254","https://openalex.org/W1596635901","https://openalex.org/W1602604383","https://openalex.org/W1687706661","https://openalex.org/W1963612623","https://openalex.org/W1963677819","https://openalex.org/W1964328938","https://openalex.org/W1965895337","https://openalex.org/W1970427994","https://openalex.org/W1979443080","https://openalex.org/W1983429394","https://openalex.org/W1987010551","https://openalex.org/W1989046305","https://openalex.org/W1993999982","https://openalex.org/W1994145105","https://openalex.org/W1995681628","https://openalex.org/W1995953909","https://openalex.org/W2004865400","https://openalex.org/W2006668994","https://openalex.org/W2006907961","https://openalex.org/W2007016988","https://openalex.org/W2007645219","https://openalex.org/W2009568626","https://openalex.org/W2009842204","https://openalex.org/W2011428301","https://openalex.org/W2014549466","https://openalex.org/W2015194506","https://openalex.org/W2017224143","https://openalex.org/W2026899601","https://openalex.org/W2030617114","https://openalex.org/W2031316969","https://openalex.org/W2033468445","https://openalex.org/W2033882205","https://openalex.org/W2038918367","https://openalex.org/W2043784721","https://openalex.org/W2044414647","https://openalex.org/W2045069146","https://openalex.org/W2045418241","https://openalex.org/W2047309768","https://openalex.org/W2051331055","https://openalex.org/W2051868937","https://openalex.org/W2052138618","https://openalex.org/W2052498615","https://openalex.org/W2052897608","https://openalex.org/W2055667610","https://openalex.org/W2056773849","https://openalex.org/W2061175874","https://openalex.org/W2063610029","https://openalex.org/W2063727277","https://openalex.org/W2063800175","https://openalex.org/W2064036576","https://openalex.org/W2064599532","https://openalex.org/W2074250616","https://openalex.org/W2077143197","https://openalex.org/W2080880708","https://openalex.org/W2096165789","https://openalex.org/W2096664104","https://openalex.org/W2100025012","https://openalex.org/W2100457950","https://openalex.org/W2111090476","https://openalex.org/W2114281708","https://openalex.org/W2117755199","https://openalex.org/W2121045282","https://openalex.org/W2134166909","https://openalex.org/W2136107095","https://openalex.org/W2145203484","https://openalex.org/W2157769293","https://openalex.org/W2163096174","https://openalex.org/W2232740620","https://openalex.org/W2352459590","https://openalex.org/W2352557913","https://openalex.org/W2416650832","https://openalex.org/W2434569190","https://openalex.org/W2491432581","https://openalex.org/W2499848210","https://openalex.org/W2505829934","https://openalex.org/W2581791419","https://openalex.org/W2738540242","https://openalex.org/W2953087027","https://openalex.org/W3021237030","https://openalex.org/W3021722416","https://openalex.org/W3216974113","https://openalex.org/W4210718478","https://openalex.org/W4246012909","https://openalex.org/W4247424088","https://openalex.org/W4250660918","https://openalex.org/W4285719527","https://openalex.org/W4292311687","https://openalex.org/W4294678829","https://openalex.org/W4298264812","https://openalex.org/W6600097003","https://openalex.org/W6600162207","https://openalex.org/W6602743192","https://openalex.org/W6604639124","https://openalex.org/W6605696842","https://openalex.org/W6606365359","https://openalex.org/W6623534408","https://openalex.org/W6630581867","https://openalex.org/W6630920308","https://openalex.org/W6635014506","https://openalex.org/W6635996023","https://openalex.org/W6639761538","https://openalex.org/W6647869205","https://openalex.org/W6652184416","https://openalex.org/W6661871859","https://openalex.org/W6663508570","https://openalex.org/W6666592450","https://openalex.org/W6674669882","https://openalex.org/W6675185510","https://openalex.org/W6676630497","https://openalex.org/W6705647010","https://openalex.org/W6705912284"],"related_works":["https://openalex.org/W1991151137","https://openalex.org/W2064003576","https://openalex.org/W3101838995","https://openalex.org/W1516031182","https://openalex.org/W2281899838","https://openalex.org/W2952735719","https://openalex.org/W3211507162","https://openalex.org/W2119063844","https://openalex.org/W2963665926","https://openalex.org/W2335222346"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":20},{"year":2016,"cited_by_count":24},{"year":2015,"cited_by_count":19},{"year":2014,"cited_by_count":27},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":32}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}
