{"id":"https://openalex.org/W42072607","doi":"https://doi.org/10.1023/a:1004570921372","title":"Equations with Singular Diffusivity","display_name":"Equations with Singular Diffusivity","publication_year":1999,"publication_date":"1999-06-01","ids":{"openalex":"https://openalex.org/W42072607","doi":"https://doi.org/10.1023/a:1004570921372","mag":"42072607"},"language":"en","primary_location":{"id":"doi:10.1023/a:1004570921372","doi":"https://doi.org/10.1023/a:1004570921372","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1004570921372","pdf_url":null,"source":{"id":"https://openalex.org/S185067381","display_name":"Journal of Statistical Physics","issn_l":"0022-4715","issn":["0022-4715","1572-9613"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Statistical Physics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2115/69170","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019169275","display_name":"Ryo Kobayashi","orcid":"https://orcid.org/0000-0001-8244-5844","observed_orcids":["https://orcid.org/0000-0001-8244-5844","https://orcid.org/0000-0002-9369-5475","https://orcid.org/0000-0003-0750-5848"]},"institutions":[{"id":"https://openalex.org/I205349734","display_name":"Hokkaido University","ror":"https://ror.org/02e16g702","country_code":"JP","type":"education","lineage":["https://openalex.org/I205349734"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"R. Kobayashi","raw_affiliation_strings":["Research Institute for Electronic Science, Hokkaido University, Sapporo, 060, Japan","Research Institute for Electronic Science, Hokkaido University , Sapporo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Institute for Electronic Science, Hokkaido University, Sapporo, 060, Japan","institution_ids":["https://openalex.org/I205349734"]},{"raw_affiliation_string":"Research Institute for Electronic Science, Hokkaido University , Sapporo, Japan","institution_ids":["https://openalex.org/I205349734"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071130497","display_name":"Yoshikazu Giga","orcid":"https://orcid.org/0000-0003-3048-5240","observed_orcids":["https://orcid.org/0000-0003-3048-5240"]},"institutions":[{"id":"https://openalex.org/I205349734","display_name":"Hokkaido University","ror":"https://ror.org/02e16g702","country_code":"JP","type":"education","lineage":["https://openalex.org/I205349734"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Y. Giga","raw_affiliation_strings":["Department of Mathematics, Hokkaido University, Sapporo, 060, Japan","Department of Mathematics, Hokkaido University, Sapporo,  Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hokkaido University, Sapporo, 060, Japan","institution_ids":["https://openalex.org/I205349734"]},{"raw_affiliation_string":"Department of Mathematics, Hokkaido University, Sapporo,  Japan","institution_ids":["https://openalex.org/I205349734"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I205349734"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":3.7176,"has_fulltext":true,"cited_by_count":99,"citation_normalized_percentile":{"value":0.93073335,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"95","issue":"5-6","first_page":"1187","last_page":"1220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.47679999470710754,"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"}},"topics":[{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.47679999470710754,"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"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.4092000126838684,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0284000001847744,"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/faceted-crystal-growth","display_name":"faceted crystal growth","score":0.7450000047683716},{"id":"https://openalex.org/keywords/grain-boundaries","display_name":"grain boundaries","score":0.9599999785423279},{"id":"https://openalex.org/keywords/gradient-systems","display_name":"gradient systems","score":0.7950000166893005},{"id":"https://openalex.org/keywords/nonlocal-interactions","display_name":"nonlocal interactions","score":0.6159999966621399}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.563077449798584},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5477298498153687},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5050385594367981},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4777076244354248},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.45126888155937195},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.43447184562683105},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.43203625082969666},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4125269055366516},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.39313358068466187},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.23380663990974426},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20528829097747803},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17882880568504333},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09240034222602844},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08985766768455505},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1023/a:1004570921372","doi":"https://doi.org/10.1023/a:1004570921372","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1004570921372","pdf_url":null,"source":{"id":"https://openalex.org/S185067381","display_name":"Journal of Statistical Physics","issn_l":"0022-4715","issn":["0022-4715","1572-9613"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Statistical Physics","raw_type":"journal-article"},{"id":"pmh:oai:EPrintsHUMATH:604","doi":null,"is_oa":false,"landing_page_url":"http://eprints3.math.sci.hokudai.ac.jp/604/1/420.PDF","pdf_url":"http://eprints3.math.sci.hokudai.ac.jp/604/1/420.PDF","source":{"id":"https://openalex.org/S4406922805","display_name":"EPrints - Department of Mathematics, Hokkaido University","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Preprint Series of Department of Mathematics, Hokkaido University","raw_type":"Preprint"},{"id":"pmh:oai:eprints.lib.hokudai.ac.jp:2115/69170","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/2115/69170","pdf_url":"http://hdl.handle.net/2115/69170","source":{"id":"https://openalex.org/S4306400549","display_name":"Hokkaido University Collection of Scholarly and Academic Papers (Hokkaido University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205349734","host_organization_name":"Hokkaido University","host_organization_lineage":["https://openalex.org/I205349734"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"bulletin (article)"},{"id":"pmh:oai:irdb.nii.ac.jp:01364:0000892790","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/2115/69170","pdf_url":"https://eprints.lib.hokudai.ac.jp/repo/huscap/all/69170/re420.pdf","source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Hokkaido University Preprint Series in Mathematics","raw_type":"departmental bulletin paper"},{"id":"mag:270816361","doi":null,"is_oa":false,"landing_page_url":"https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69170/1/pre420.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306523113","display_name":"Preprint Series of Department of Mathematics, Hokkaido University","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Preprint Series of Department of Mathematics, Hokkaido University","raw_type":null}],"best_oa_location":{"id":"pmh:oai:eprints.lib.hokudai.ac.jp:2115/69170","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/2115/69170","pdf_url":"http://hdl.handle.net/2115/69170","source":{"id":"https://openalex.org/S4306400549","display_name":"Hokkaido University Collection of Scholarly and Academic Papers (Hokkaido University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205349734","host_organization_name":"Hokkaido University","host_organization_lineage":["https://openalex.org/I205349734"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"bulletin (article)"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Affordable and clean energy","score":0.8799999952316284,"id":"https://metadata.un.org/sdg/7"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W42072607.pdf"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W588153840","https://openalex.org/W1563676637","https://openalex.org/W1981412090","https://openalex.org/W1998937828","https://openalex.org/W2015873351","https://openalex.org/W2030708989","https://openalex.org/W2057958367","https://openalex.org/W2062314820","https://openalex.org/W2063699913","https://openalex.org/W2063800770","https://openalex.org/W2108056018","https://openalex.org/W2167476690","https://openalex.org/W4244502344"],"related_works":["https://openalex.org/W42295635","https://openalex.org/W1973996291","https://openalex.org/W1598955744","https://openalex.org/W2330575325","https://openalex.org/W4388747848","https://openalex.org/W2163803519","https://openalex.org/W2497592525","https://openalex.org/W4384111961","https://openalex.org/W3096145648","https://openalex.org/W4285167822"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":5}],"updated_date":"2026-10-13T10:08:12.033832","created_date":"2016-06-24T00:00:00"}