{"id":"https://openalex.org/W2987353995","doi":"https://doi.org/10.1137/19m1300017","title":"The Waiting Time Phenomenon in Spatially Discretized Porous Medium and Thin Film Equations","display_name":"The Waiting Time Phenomenon in Spatially Discretized Porous Medium and Thin Film Equations","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2987353995","doi":"https://doi.org/10.1137/19m1300017","mag":"2987353995"},"language":"en","primary_location":{"id":"doi:10.1137/19m1300017","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1300017","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1911.04185","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027403115","display_name":"Julian Fischer","orcid":"https://orcid.org/0000-0002-0479-558X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Julian Fischer","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040660166","display_name":"Daniel Matthes","orcid":"https://orcid.org/0000-0001-6764-8301"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Matthes","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027403115"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0121034,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"1","first_page":"60","last_page":"87"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9986000061035156,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9986000061035156,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9955999851226807,"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/discretization","display_name":"Discretization","score":0.8223382830619812},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.6740479469299316},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5419725775718689},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5078538060188293},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.5014848709106445},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.43288475275039673},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42402809858322144},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.3259367346763611},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25257229804992676},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.1516527235507965}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8223382830619812},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.6740479469299316},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5419725775718689},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5078538060188293},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5014848709106445},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.43288475275039673},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42402809858322144},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.3259367346763611},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25257229804992676},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.1516527235507965},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/19m1300017","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1300017","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1911.04185","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.04185","pdf_url":"https://arxiv.org/pdf/1911.04185","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2987353995","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1911.04185","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1911.04185","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1911.04185","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1911.04185","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.04185","pdf_url":"https://arxiv.org/pdf/1911.04185","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.41999998688697815}],"awards":[{"id":"https://openalex.org/G6773318802","display_name":null,"funder_award_id":"TRR 109","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2987353995.pdf","grobid_xml":"https://content.openalex.org/works/W2987353995.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W299665525","https://openalex.org/W1494768298","https://openalex.org/W1522579744","https://openalex.org/W1579958463","https://openalex.org/W1864129253","https://openalex.org/W1964889848","https://openalex.org/W1974213952","https://openalex.org/W1987047421","https://openalex.org/W1988974595","https://openalex.org/W2006369296","https://openalex.org/W2006838499","https://openalex.org/W2017258417","https://openalex.org/W2032254325","https://openalex.org/W2032994472","https://openalex.org/W2044163325","https://openalex.org/W2045175626","https://openalex.org/W2045972093","https://openalex.org/W2049585229","https://openalex.org/W2054723044","https://openalex.org/W2055054359","https://openalex.org/W2058436955","https://openalex.org/W2060052509","https://openalex.org/W2066908036","https://openalex.org/W2078279585","https://openalex.org/W2081193816","https://openalex.org/W2089832669","https://openalex.org/W2092683400","https://openalex.org/W2094027993","https://openalex.org/W2119761103","https://openalex.org/W2122036088","https://openalex.org/W2158169385","https://openalex.org/W2228396941","https://openalex.org/W2254295889","https://openalex.org/W2549442543","https://openalex.org/W2566375847","https://openalex.org/W2821775784","https://openalex.org/W2960988475","https://openalex.org/W3101192369"],"related_works":["https://openalex.org/W1973191545","https://openalex.org/W1652563640","https://openalex.org/W2613657454","https://openalex.org/W2951511248","https://openalex.org/W1524323972","https://openalex.org/W2089564974","https://openalex.org/W2029183995","https://openalex.org/W2781610065","https://openalex.org/W3264880","https://openalex.org/W3130288359","https://openalex.org/W3004013355","https://openalex.org/W2119890550","https://openalex.org/W2037299237","https://openalex.org/W2741110232","https://openalex.org/W2030416203","https://openalex.org/W576106123","https://openalex.org/W2004239158","https://openalex.org/W242124940","https://openalex.org/W1548133290","https://openalex.org/W8858050"],"abstract_inverted_index":{"Various":[0],"degenerate":[1],"diffusion":[2],"equations":[3],"exhibit":[4],"a":[5,34,92,104,112],"waiting":[6,68,87],"time":[7,88,114],"phenomenon:":[8],"depending":[9],"on":[10,120,122,144],"the":[11,14,20,23,25,28,51,55,65,74,78,82,86,95,108,123,152],"\u201cflatness\u201d":[12],"of":[13,22,27,37,50,67,94,97],"compactly":[15],"supported":[16],"initial":[17],"datum":[18],"at":[19],"boundary":[21,146],"support,":[24],"support":[26,98],"solution":[29],"may":[30],"not":[31],"expand":[32],"for":[33,64,77,158],"certain":[35],"amount":[36],"time.":[38],"We":[39],"show":[40,150],"that":[41,70,151],"this":[42],"phenomenon":[43,89,153],"is":[44,118,154],"captured":[45],"by":[46,103],"particular":[47],"Lagrangian":[48,127],"discretizations":[49],"porous":[52],"medium":[53],"and":[54,59],"thin":[56],"film":[57],"equations,":[58],"we":[60],"obtain":[61],"sufficient":[62],"criteria":[63],"occurrence":[66],"times":[69],"are":[71],"consistent":[72],"with":[73,133],"known":[75],"ones":[76],"original":[79,101],"PDEs.":[80],"For":[81],"spatially":[83],"discrete":[84],"solution,":[85],"refers":[90],"to":[91,107,141],"deviation":[93],"edge":[96],"from":[99],"its":[100],"position":[102],"quantity":[105],"comparable":[106],"mesh":[109],"width,":[110],"over":[111],"mesh-independent":[113],"interval.":[115],"Our":[116],"proof":[117],"based":[119],"estimates":[121,132],"fluid":[124],"velocity":[125],"in":[126],"coordinates.":[128],"Combining":[129],"weighted":[130],"entropy":[131],"an":[134],"iteration":[135],"technique":[136],"\u00e0":[137],"la":[138],"Stampacchia":[139],"leads":[140],"upper":[142],"bounds":[143],"free":[145],"propagation.":[147],"Numerical":[148],"simulations":[149],"already":[155],"clearly":[156],"visible":[157],"relatively":[159],"coarse":[160],"discretizations.":[161]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}