{"id":"https://openalex.org/W2049314201","doi":"https://doi.org/10.1007/s002080010010","title":"Rigorous Numerics for Partial Differential Equations: The Kuramoto\u2014Sivashinsky Equation","display_name":"Rigorous Numerics for Partial Differential Equations: The Kuramoto\u2014Sivashinsky Equation","publication_year":2001,"publication_date":"2001-07-01","ids":{"openalex":"https://openalex.org/W2049314201","doi":"https://doi.org/10.1007/s002080010010","mag":"2049314201"},"language":"en","primary_location":{"id":"doi:10.1007/s002080010010","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002080010010","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ruj.uj.edu.pl/xmlui/handle/item/80211","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085109355","display_name":"Piotr Zgliczy\u0144ski","orcid":"https://orcid.org/0000-0002-4852-0887"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Piotr Zgliczynski","raw_affiliation_strings":["Jagiellonian University Institute of Mathematics Reymonta 4 30-059 Krak\u00f3w, Poland zgliczyn@im.uj.edu.pl, PL","Jagiellonian University Institute of Mathematics Reymonta 4 30-059 Krak\u00f3w, Poland zgliczyn@im.uj.edu.pl"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jagiellonian University Institute of Mathematics Reymonta 4 30-059 Krak\u00f3w, Poland zgliczyn@im.uj.edu.pl, PL","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"Jagiellonian University Institute of Mathematics Reymonta 4 30-059 Krak\u00f3w, Poland zgliczyn@im.uj.edu.pl","institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210137370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049298090","display_name":"Konstantin Mischaikow","orcid":"https://orcid.org/0000-0003-2876-4558"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Konstantin Mischaikow","raw_affiliation_strings":["Center for Dynamical Systems and Nonlinear Studies School of Mathematics Georgia Institute of Technology Atlanta, GA 30332, USA mischaik@math.gatech.edu, US","Center for Dynamical Systems and Nonlinear Studies School of Mathematics Georgia Institute of Technology Atlanta, GA 30332, USA mischaik@math.gatech.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Dynamical Systems and Nonlinear Studies School of Mathematics Georgia Institute of Technology Atlanta, GA 30332, USA mischaik@math.gatech.edu, US","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Center for Dynamical Systems and Nonlinear Studies School of Mathematics Georgia Institute of Technology Atlanta, GA 30332, USA mischaik@math.gatech.edu","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085109355"],"corresponding_institution_ids":["https://openalex.org/I126596746","https://openalex.org/I4210137370"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":4.0197,"has_fulltext":false,"cited_by_count":124,"citation_normalized_percentile":{"value":0.94602543,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"1","issue":"3","first_page":"255","last_page":"288"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9972000122070312,"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"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9972000122070312,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9861999750137329,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.877253532409668},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.659233808517456},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6553698182106018},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6201022863388062},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.5992139577865601},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5723168849945068},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.4842069149017334},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43080225586891174},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4167737066745758},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3730432987213135},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1496654450893402}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.877253532409668},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.659233808517456},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6553698182106018},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6201022863388062},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.5992139577865601},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5723168849945068},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.4842069149017334},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43080225586891174},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4167737066745758},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3730432987213135},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1496654450893402},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s002080010010","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002080010010","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:ruj.uj.edu.pl:item/80211","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/xmlui/handle/item/80211","pdf_url":null,"source":{"id":"https://openalex.org/S4306400316","display_name":"Homo Politicus (Academy of Humanities and Economics in Lodz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"artyku\u0142 w czasopi\u015bmie"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.33.9725","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.9725","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.gatech.edu/~mischaik/papers/kuramoto.ps","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:ruj.uj.edu.pl:item/80211","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/xmlui/handle/item/80211","pdf_url":null,"source":{"id":"https://openalex.org/S4306400316","display_name":"Homo Politicus (Academy of Humanities and Economics in Lodz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"artyku\u0142 w czasopi\u015bmie"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W162901799","https://openalex.org/W409831783","https://openalex.org/W1485705023","https://openalex.org/W1511670820","https://openalex.org/W1557040331","https://openalex.org/W1594759473","https://openalex.org/W1982999858","https://openalex.org/W1986250193","https://openalex.org/W1995551283","https://openalex.org/W2002970251","https://openalex.org/W2018960775","https://openalex.org/W2038991247","https://openalex.org/W2072958652","https://openalex.org/W2077510959","https://openalex.org/W2101628805","https://openalex.org/W2139886236","https://openalex.org/W2260570520","https://openalex.org/W2433005247"],"related_works":["https://openalex.org/W3082668976","https://openalex.org/W2517973022","https://openalex.org/W1543121148","https://openalex.org/W1580703421","https://openalex.org/W2618518959","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W4382202915","https://openalex.org/W4288093367","https://openalex.org/W2489516236"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2026-05-03T08:25:01.440150","created_date":"2025-10-10T00:00:00"}
