{"id":"https://openalex.org/W2740498180","doi":"https://doi.org/10.1137/17m1141485","title":"Self-Similar Lifting and Persistent Touch-Down Points in the Thin-Film Equation","display_name":"Self-Similar Lifting and Persistent Touch-Down Points in the Thin-Film Equation","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2740498180","doi":"https://doi.org/10.1137/17m1141485","mag":"2740498180"},"language":"en","primary_location":{"id":"doi:10.1137/17m1141485","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1141485","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/A5055276708","display_name":"Carlota M. Cuesta","orcid":"https://orcid.org/0000-0001-7297-7652"},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Carlota M. Cuesta","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Faculty of Science and Technology, University of the Basque Country (UPV/EHU),"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Faculty of Science and Technology, University of the Basque Country (UPV/EHU),","institution_ids":["https://openalex.org/I169108374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063813071","display_name":"Hans Kn\u00fcpfer","orcid":"https://orcid.org/0000-0002-5861-772X"},"institutions":[{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hans Kn\u00fcpfer","raw_affiliation_strings":["IWR, Universit\u00e4t Heidelberg,","Institut f\u00fcr Angewandte Mathematik,"],"affiliations":[{"raw_affiliation_string":"IWR, Universit\u00e4t Heidelberg,","institution_ids":["https://openalex.org/I223822909"]},{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik,","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048197687","display_name":"Juan J. L. Vel\u00e1zquez","orcid":"https://orcid.org/0000-0002-7397-5525"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Juan J. L. Vel\u00e1zquez","raw_affiliation_strings":["Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn,"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn,","institution_ids":["https://openalex.org/I135140700"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055276708"],"corresponding_institution_ids":["https://openalex.org/I169108374"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00432028,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"50","issue":"2","first_page":"1900","last_page":"1917"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9998999834060669,"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":0.9998999834060669,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7470036745071411},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5321860313415527},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5005700588226318},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.4270499348640442},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.28860101103782654}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7470036745071411},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5321860313415527},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5005700588226318},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.4270499348640442},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.28860101103782654},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1141485","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1141485","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":[{"id":"https://metadata.un.org/sdg/10","score":0.41999998688697815,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1497218953","display_name":null,"funder_award_id":"Spanish","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G1693977860","display_name":null,"funder_award_id":"MTM2014-53145-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G3655418302","display_name":null,"funder_award_id":"CRC 1060","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G560801653","display_name":null,"funder_award_id":"IT641-13","funder_id":"https://openalex.org/F4320321705","funder_display_name":"Eusko Jaurlaritza"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321705","display_name":"Eusko Jaurlaritza","ror":"https://ror.org/00pz2fp31"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1494768298","https://openalex.org/W1971723555","https://openalex.org/W1978198939","https://openalex.org/W1979080982","https://openalex.org/W1988974595","https://openalex.org/W2032994472","https://openalex.org/W2048285539","https://openalex.org/W2049585229","https://openalex.org/W2055054359","https://openalex.org/W2058436955","https://openalex.org/W2062114509","https://openalex.org/W2078279585","https://openalex.org/W2080372279","https://openalex.org/W2083250674","https://openalex.org/W2087522722","https://openalex.org/W2089964069","https://openalex.org/W2092683400","https://openalex.org/W2115463092","https://openalex.org/W2115619789","https://openalex.org/W2119283405","https://openalex.org/W2147327725","https://openalex.org/W2157275667","https://openalex.org/W2158169385","https://openalex.org/W2254295889","https://openalex.org/W2964102765","https://openalex.org/W3091963029","https://openalex.org/W3101192369","https://openalex.org/W4254216534"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"We":[0],"study":[1,84],"self-similar":[2,79],"solutions":[3,60],"of":[4,30,40,51,77,93,101],"the":[5,28,41,52,75,78,99],"thin-film":[6,53],"equation":[7,54],"$":[8,21],"h_{t}":[9],"+":[10],"(h^{m}":[11],"h_{xxx})_{x}":[12],"=":[13],"0":[14,19],"\\":[15],"{in}\\":[16],"\\{(x,t):h(x,t)":[17],">":[18],"\\}":[20],"with":[22,55,61],"$m":[23,56],"\\in":[24,57],"(0,4]$":[25],"that":[26],"describe":[27],"lifting":[29],"an":[31,37],"isolated":[32],"touch-down":[33,64],"point":[34,65],"given":[35],"by":[36],"initial":[38],"profile":[39],"form":[42],"$h_{in}(x)=":[43],"|x|$.":[44],"This":[45],"provides":[46],"a":[47,62,85,94],"mechanism":[48],"for":[49],"nonuniqueness":[50],"(2,4)$":[58],"since":[59],"persistent":[63],"also":[66],"exist":[67],"in":[68],"this":[69],"case.":[70],"In":[71],"order":[72],"to":[73,83],"prove":[74],"existence":[76],"solutions,":[80],"we":[81],"need":[82],"four-dimensional":[86],"continuous":[87],"dynamical":[88],"system.":[89],"The":[90],"proof":[91],"consists":[92],"shooting":[95],"argument":[96],"based":[97],"on":[98,105],"identification":[100],"invariant":[102],"regions":[103],"and":[104],"suitable":[106],"energy":[107],"formulas.":[108]},"counts_by_year":[],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}
