{"id":"https://openalex.org/W2012153215","doi":"https://doi.org/10.1137/s0036141099350894","title":"Existence of Undercompressive Traveling Waves in Thin Film Equations","display_name":"Existence of Undercompressive Traveling Waves in Thin Film Equations","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2012153215","doi":"https://doi.org/10.1137/s0036141099350894","mag":"2012153215"},"language":"en","primary_location":{"id":"doi:10.1137/s0036141099350894","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141099350894","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/A5090707978","display_name":"Andrea L. Bertozzi","orcid":"https://orcid.org/0000-0003-0396-7391"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. L. Bertozzi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004685911","display_name":"Michael Shearer","orcid":"https://orcid.org/0000-0001-5404-3258"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Shearer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.437,"has_fulltext":false,"cited_by_count":74,"citation_normalized_percentile":{"value":0.95531616,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"32","issue":"1","first_page":"194","last_page":"213"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9973999857902527,"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"}},"topics":[{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9973999857902527,"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":0.9886000156402588,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9782999753952026,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.8402808904647827},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.694887101650238},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.6755578517913818},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6389490365982056},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.4385858178138733},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43562251329421997},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.4310234785079956},{"id":"https://openalex.org/keywords/flux","display_name":"Flux (metallurgy)","score":0.41927266120910645},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.4119744300842285},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.0645521879196167}],"concepts":[{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.8402808904647827},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.694887101650238},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.6755578517913818},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6389490365982056},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.4385858178138733},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43562251329421997},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.4310234785079956},{"id":"https://openalex.org/C68709404","wikidata":"https://www.wikidata.org/wiki/Q1134475","display_name":"Flux (metallurgy)","level":2,"score":0.41927266120910645},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.4119744300842285},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0645521879196167},{"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036141099350894","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036141099350894","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W14467920","https://openalex.org/W1972904407","https://openalex.org/W1979363157","https://openalex.org/W1982437157","https://openalex.org/W1993472270","https://openalex.org/W1996584940","https://openalex.org/W2000105674","https://openalex.org/W2006580718","https://openalex.org/W2006699869","https://openalex.org/W2011097024","https://openalex.org/W2012312399","https://openalex.org/W2013238203","https://openalex.org/W2017896536","https://openalex.org/W2017935165","https://openalex.org/W2038991247","https://openalex.org/W2039734675","https://openalex.org/W2043397430","https://openalex.org/W2044931545","https://openalex.org/W2049025708","https://openalex.org/W2049568698","https://openalex.org/W2051524346","https://openalex.org/W2060678577","https://openalex.org/W2062082273","https://openalex.org/W2081854106","https://openalex.org/W2086688865","https://openalex.org/W2089876099","https://openalex.org/W2090776307","https://openalex.org/W2093640811","https://openalex.org/W2111559309","https://openalex.org/W2115619789","https://openalex.org/W2120864055","https://openalex.org/W2127531437","https://openalex.org/W2138031176","https://openalex.org/W2143752850","https://openalex.org/W2165659230","https://openalex.org/W2566514124","https://openalex.org/W2607516261","https://openalex.org/W3102376713","https://openalex.org/W4285719527","https://openalex.org/W4292081050"],"related_works":["https://openalex.org/W2479314534","https://openalex.org/W4295797339","https://openalex.org/W1967450583","https://openalex.org/W198342057","https://openalex.org/W2139348706","https://openalex.org/W3015400604","https://openalex.org/W2040118937","https://openalex.org/W4235545837","https://openalex.org/W4388524987","https://openalex.org/W935007796"],"abstract_inverted_index":{"We":[0,68],"consider":[1],"undercompressive":[2,73],"traveling":[3,74],"wave":[4,75],"solutions":[5],"of":[6,50,60,71],"the":[7,23,28,48,51,66],"partial":[8],"differential":[9],"equation":[10],"$$\\partial_t":[11],"h+":[12],"\\partial_x":[13,20],"f(h)":[14,31],"=":[15,32],"-\\partial_x(h^3\\partial_x^3":[16],"h)":[17],"+":[18],"D\\partial_x(h^3":[19],"h),$$":[21],"when":[22,84],"flux":[24],"function":[25],"f":[26],"has":[27],"nonconvex":[29],"form":[30],"h2":[33],"-h3":[34],".":[35],"In":[36],"numerical":[37],"simulations,":[38],"these":[39],"waves":[40],"appear":[41],"to":[42],"play":[43],"a":[44],"central":[45],"role":[46],"in":[47,58],"dynamics":[49],"PDE;":[52],"they":[53],"also":[54],"explain":[55],"unusual":[56],"phenomena":[57],"experiments":[59],"driven":[61],"contact":[62],"lines":[63],"modeled":[64],"by":[65],"PDE.":[67],"prove":[69],"existence":[70],"an":[72],"solution":[76],"for":[77],"sufficiently":[78,87],"small":[79],"nonnegative":[80],"D":[81,85],"and":[82],"nonexistence":[83],"is":[86],"large.":[88]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}