{"id":"https://openalex.org/W1967216996","doi":"https://doi.org/10.1137/10078298x","title":"Integration of Dissipative Partial Differential Equations: A Case Study","display_name":"Integration of Dissipative Partial Differential Equations: A Case Study","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1967216996","doi":"https://doi.org/10.1137/10078298x","mag":"1967216996"},"language":"en","primary_location":{"id":"doi:10.1137/10078298x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/10078298x","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","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/A5013721577","display_name":"Gianni Arioli","orcid":"https://orcid.org/0000-0002-3646-7900"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gianni Arioli","raw_affiliation_strings":["Polytechnic University of Milan;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Polytechnic University of Milan;","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103970464","display_name":"Hans P. Koch","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hans Koch","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1935,"has_fulltext":false,"cited_by_count":57,"citation_normalized_percentile":{"value":0.8751042,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"9","issue":"3","first_page":"1119","last_page":"1133"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9980000257492065,"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":0.9980000257492065,"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":0.9973999857902527,"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":0.9613999724388123,"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/dissipative-system","display_name":"Dissipative system","score":0.8887722492218018},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.687474250793457},{"id":"https://openalex.org/keywords/hyperbolic-partial-differential-equation","display_name":"Hyperbolic partial differential equation","score":0.545074999332428},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"Periodic orbits","score":0.5001826286315918},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49312207102775574},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4860859215259552},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48606231808662415},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.46071773767471313},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.44853100180625916},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4139575958251953},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.31163835525512695}],"concepts":[{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.8887722492218018},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.687474250793457},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.545074999332428},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.5001826286315918},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49312207102775574},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4860859215259552},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48606231808662415},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.46071773767471313},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.44853100180625916},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4139575958251953},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31163835525512695},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/10078298x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/10078298x","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:re.public.polimi.it:11311/575257","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/575257","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1480333587","https://openalex.org/W1966750560","https://openalex.org/W1982999858","https://openalex.org/W1995551283","https://openalex.org/W2008486579","https://openalex.org/W2013615321","https://openalex.org/W2023892882","https://openalex.org/W2033829787","https://openalex.org/W2045720672","https://openalex.org/W2046527278","https://openalex.org/W2048280869","https://openalex.org/W2049314201","https://openalex.org/W2139886236","https://openalex.org/W2335062971","https://openalex.org/W4213080596","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2123186262","https://openalex.org/W2544961282","https://openalex.org/W3113785985","https://openalex.org/W2512568578","https://openalex.org/W2065775687","https://openalex.org/W2009729781","https://openalex.org/W39293662","https://openalex.org/W2272074809","https://openalex.org/W1967216996","https://openalex.org/W2093617977"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,15,33],"computer-assisted":[3],"technique":[4],"for":[5,26],"constructing":[6],"and":[7],"analyzing":[8],"orbits":[9],"of":[10,32],"dissipative":[11],"evolution":[12],"equations.":[13],"As":[14],"case":[16],"study,":[17],"the":[18,23,30],"methods":[19],"are":[20],"applied":[21],"to":[22],"Kuramoto\u2013Sivashinski":[24],"equation,":[25],"which":[27],"we":[28],"prove":[29],"existence":[31],"hyperbolic":[34],"periodic":[35],"orbit.":[36]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
