{"id":"https://openalex.org/W7222160658","doi":"https://doi.org/10.48550/arxiv.2610.19086","title":"Sharp Convergence Rate for stationary states of the Porous Medium Equation","display_name":"Sharp Convergence Rate for stationary states of the Porous Medium Equation","publication_year":2026,"publication_date":"2026-10-13","ids":{"openalex":"https://openalex.org/W7222160658","doi":"https://doi.org/10.48550/arxiv.2610.19086"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.19086","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.19086","pdf_url":"https://arxiv.org/pdf/2610.19086","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.19086","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123630004","display_name":"Igor Pinheiro","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Pinheiro, Igor","raw_affiliation_strings":["Dipartimento di Matematica e Informatica \"Ulisse Dini\" , Universit\u00e0 degli Studi di Firenze","Universit\u00e9 Lyon"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica \"Ulisse Dini\" , Universit\u00e0 degli Studi di Firenze","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Universit\u00e9 Lyon","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022440462","display_name":"Filippo Santambrogio","orcid":"https://orcid.org/0000-0002-3333-1127","observed_orcids":["https://orcid.org/0000-0002-3333-1127"]},"institutions":[{"id":"https://openalex.org/I112936343","display_name":"\u00c9cole Centrale de Lyon","ror":"https://ror.org/05s6rge65","country_code":"FR","type":"education","lineage":["https://openalex.org/I112936343","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]},{"id":"https://openalex.org/I4405259976","display_name":"Universit\u00e9 Jean Monnet","ror":"https://ror.org/030bahv93","country_code":"FR","type":"education","lineage":["https://openalex.org/I203339264","https://openalex.org/I4405259976"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]},{"id":"https://openalex.org/I48430043","display_name":"Institut National des Sciences Appliqu\u00e9es de Lyon","ror":"https://ror.org/050jn9y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I203339264","https://openalex.org/I48430043"]},{"id":"https://openalex.org/I86767153","display_name":"Universit\u00e9 Jean Monnet","ror":"https://ror.org/04yznqr36","country_code":"FR","type":"education","lineage":["https://openalex.org/I203339264","https://openalex.org/I4405259976","https://openalex.org/I86767153"]}],"countries":["FR","IT"],"is_corresponding":false,"raw_author_name":"Santambrogio, Filippo","raw_affiliation_strings":[", Ecole Centrale de Lyon , INSA Lyon , Universit\u00e9 Jean Monnet , CNRS , ICJ , UMR 5208 , Villeurbanne , France","Dipartimento di Matematica e Informatica \"Ulisse Dini\" , Universit\u00e0 degli Studi di Firenze"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":", Ecole Centrale de Lyon , INSA Lyon , Universit\u00e9 Jean Monnet , CNRS , ICJ , UMR 5208 , Villeurbanne , France","institution_ids":["https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043","https://openalex.org/I86767153"]},{"raw_affiliation_string":"Dipartimento di Matematica e Informatica \"Ulisse Dini\" , Universit\u00e0 degli Studi di Firenze","institution_ids":["https://openalex.org/I45084792"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9848999977111816,"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"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9848999977111816,"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"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.012799999676644802,"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"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/porous-medium-equation","display_name":"porous medium equation","score":0.9940000176429749},{"id":"https://openalex.org/keywords/stationary-states","display_name":"stationary states","score":0.8880000114440918},{"id":"https://openalex.org/keywords/external-drift","display_name":"external drift","score":0.9399999976158142},{"id":"https://openalex.org/keywords/potential","display_name":"potential","score":0.41499999165534973},{"id":"https://openalex.org/keywords/nonlocal-diffusion","display_name":"nonlocal diffusion","score":0.382999986410141}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6164000034332275},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.5954999923706055},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5476999878883362},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5440999865531921},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5121999979019165},{"id":"https://openalex.org/C47458137","wikidata":"https://www.wikidata.org/wiki/Q911951","display_name":"Stationary state","level":2,"score":0.5095999836921692},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4440999925136566},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3418000042438507},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3222000002861023},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C110405555","wikidata":"https://www.wikidata.org/wiki/Q1192209","display_name":"Stationary process","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C2777634741","wikidata":"https://www.wikidata.org/wiki/Q768993","display_name":"Wasserstein metric","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.2874000072479248},{"id":"https://openalex.org/C111163200","wikidata":"https://www.wikidata.org/wiki/Q904041","display_name":"Rate equation","level":3,"score":0.2802000045776367},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.2590000033378601},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.19086","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.19086","pdf_url":"https://arxiv.org/pdf/2610.19086","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.19086","doi":"https://doi.org/10.48550/arxiv.2610.19086","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.19086","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.19086","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.19086","pdf_url":"https://arxiv.org/pdf/2610.19086","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222160658.pdf","grobid_xml":"https://content.openalex.org/works/W7222160658.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2080676466"],"related_works":["https://openalex.org/W1703546963","https://openalex.org/W7099125653","https://openalex.org/W4407092961","https://openalex.org/W50461372","https://openalex.org/W7095416081","https://openalex.org/W7097539591","https://openalex.org/W7046881058","https://openalex.org/W4226146757","https://openalex.org/W1692322820","https://openalex.org/W7097547642"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"prove":[4],"the":[5,14,23,31],"sharp":[6],"rate":[7],"of":[8,13],"convergence":[9],"for":[10,34],"stationary":[11],"states":[12],"porous":[15],"medium":[16],"equation":[17],"with":[18],"an":[19],"external":[20],"drift":[21],"in":[22],"p-Wasserstein":[24],"metric":[25],"under":[26],"very":[27],"mild":[28],"assumptions":[29],"on":[30],"potential":[32],"and":[33],"any":[35],"$1\\leq":[36],"p\\leq":[37],"+\\infty$.":[38]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-16T00:00:00"}
