{"id":"https://openalex.org/W2087285759","doi":"https://doi.org/10.1137/080714178","title":"Mesenchymal Motion Models in One Dimension","display_name":"Mesenchymal Motion Models in One Dimension","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2087285759","doi":"https://doi.org/10.1137/080714178","mag":"2087285759"},"language":"en","primary_location":{"id":"doi:10.1137/080714178","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080714178","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/A5031464759","display_name":"Zhi\u2010An Wang","orcid":"https://orcid.org/0000-0003-2945-5810"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"id":"https://openalex.org/I4210101327","display_name":"Twin Cities Orthopedics","ror":"https://ror.org/01en4s460","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210101327"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhi-An Wang","raw_affiliation_strings":["University of Minnesota Twin Cities"],"affiliations":[{"raw_affiliation_string":"University of Minnesota Twin Cities","institution_ids":["https://openalex.org/I4210101327","https://openalex.org/I130238516"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050122860","display_name":"Thomas Hillen","orcid":"https://orcid.org/0000-0003-0819-9520"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Thomas Hillen","raw_affiliation_strings":["University of Alberta"],"affiliations":[{"raw_affiliation_string":"University of Alberta","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100724525","display_name":"Michael Li","orcid":"https://orcid.org/0000-0003-1853-3537"},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Michael Li","raw_affiliation_strings":["University of Alberta"],"affiliations":[{"raw_affiliation_string":"University of Alberta","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5031464759"],"corresponding_institution_ids":["https://openalex.org/I130238516","https://openalex.org/I4210101327"],"apc_list":null,"apc_paid":null,"fwci":0.541,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.72157773,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"69","issue":"2","first_page":"375","last_page":"397"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10492","display_name":"Microtubule and mitosis dynamics","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10379","display_name":"Cellular Mechanics and Interactions","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/1307","display_name":"Cell Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.6537039875984192},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5708295106887817},{"id":"https://openalex.org/keywords/mesenchymal-stem-cell","display_name":"Mesenchymal stem cell","score":0.5591245293617249},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.545403003692627},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5012726783752441},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.47899600863456726},{"id":"https://openalex.org/keywords/carry","display_name":"Carry (investment)","score":0.44069704413414},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41897037625312805},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36464518308639526},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.36058008670806885},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.27729713916778564},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2632513642311096},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.08765241503715515}],"concepts":[{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.6537039875984192},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5708295106887817},{"id":"https://openalex.org/C198826908","wikidata":"https://www.wikidata.org/wiki/Q1922379","display_name":"Mesenchymal stem cell","level":2,"score":0.5591245293617249},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.545403003692627},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5012726783752441},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.47899600863456726},{"id":"https://openalex.org/C2776299755","wikidata":"https://www.wikidata.org/wiki/Q432449","display_name":"Carry (investment)","level":2,"score":0.44069704413414},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41897037625312805},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36464518308639526},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.36058008670806885},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27729713916778564},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2632513642311096},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.08765241503715515},{"id":"https://openalex.org/C95444343","wikidata":"https://www.wikidata.org/wiki/Q7141","display_name":"Cell biology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/080714178","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080714178","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.433.6388","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.433.6388","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ualberta.ca/~thillen/paper/onedmesen.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W16559667","https://openalex.org/W247481854","https://openalex.org/W1493195308","https://openalex.org/W1510122527","https://openalex.org/W1523377158","https://openalex.org/W1585999563","https://openalex.org/W1967166599","https://openalex.org/W1981825355","https://openalex.org/W1994800451","https://openalex.org/W1994849592","https://openalex.org/W1999582860","https://openalex.org/W2001019345","https://openalex.org/W2012058749","https://openalex.org/W2023735315","https://openalex.org/W2027098220","https://openalex.org/W2036591697","https://openalex.org/W2058760931","https://openalex.org/W2069956540","https://openalex.org/W2090565769","https://openalex.org/W2094495898","https://openalex.org/W2101750222","https://openalex.org/W2126852138","https://openalex.org/W2137420983","https://openalex.org/W2139656224","https://openalex.org/W2169659086","https://openalex.org/W2338523630","https://openalex.org/W2753844715"],"related_works":["https://openalex.org/W4229867111","https://openalex.org/W2793180915","https://openalex.org/W2386495035","https://openalex.org/W1582047458","https://openalex.org/W1514266315","https://openalex.org/W2071291085","https://openalex.org/W1490628945","https://openalex.org/W2115529833","https://openalex.org/W2113094707","https://openalex.org/W4244565034"],"abstract_inverted_index":{"Mesenchymal":[0],"motion":[1,51],"denotes":[2],"a":[3,28,44],"form":[4,33],"of":[5,34,47,58,68,79,97],"cell":[6],"movement":[7,35],"through":[8],"tissue":[9],"which":[10],"can":[11],"be":[12],"observed":[13],"for":[14,31],"certain":[15],"cancer":[16],"metastases.":[17],"In":[18,38],"[T.":[19],"Hillen,":[20],"J.":[21],"Math.":[22],"Biol.,":[23],"53":[24],"(2006),":[25],"pp.":[26],"585\u2013616],":[27],"mathematical":[29],"model":[30],"this":[32],"was":[36],"introduced.":[37],"the":[39,48,55,65,69,73,77,89,94,98],"current":[40],"paper":[41],"we":[42,92],"present":[43],"comprehensive":[45],"analysis":[46],"one-dimensional":[49],"mesenchymal":[50],"model.":[52,70],"We":[53,71],"establish":[54],"global":[56],"existence":[57,78],"classical":[59],"solutions":[60],"and":[61,83],"rigorously":[62],"carry":[63],"out":[64],"parabolic":[66],"limit":[67],"discuss":[72,93],"stationary":[74],"solutions,":[75,82],"prove":[76],"traveling":[80],"wave":[81],"use":[84],"numerical":[85],"simulations":[86],"to":[87],"illustrate":[88],"results.":[90,99],"Finally,":[91],"biological":[95],"implications":[96]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
