{"id":"https://openalex.org/W2005761796","doi":"https://doi.org/10.1137/030600515","title":"Freezing Solutions of Equivariant Evolution Equations","display_name":"Freezing Solutions of Equivariant Evolution Equations","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2005761796","doi":"https://doi.org/10.1137/030600515","mag":"2005761796"},"language":"en","primary_location":{"id":"doi:10.1137/030600515","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030600515","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/A5079432529","display_name":"Wolf-J\u00fcergen Beyn","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"W. J. Beyn","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006835306","display_name":"Vera Th\u00fcmmler","orcid":null},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"V. Th\u00fcmmler","raw_affiliation_strings":["Bielefeld University,;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bielefeld University,;","institution_ids":["https://openalex.org/I20121455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8364,"has_fulltext":false,"cited_by_count":101,"citation_normalized_percentile":{"value":0.92572767,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"3","issue":"2","first_page":"85","last_page":"116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9977999925613403,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9977999925613403,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9965000152587891,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9957000017166138,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7763110995292664},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.6030769944190979},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5175042152404785},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.4979212284088135},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.49412110447883606},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4872812032699585},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4501868188381195},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.42822080850601196},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4193931818008423},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.41507619619369507},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4008139371871948},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.09604838490486145}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7763110995292664},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.6030769944190979},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5175042152404785},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.4979212284088135},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.49412110447883606},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4872812032699585},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4501868188381195},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.42822080850601196},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4193931818008423},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.41507619619369507},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4008139371871948},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.09604838490486145},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/030600515","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030600515","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:CiteSeerX.psu:10.1.1.484.1984","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.484.1984","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathematik.uni-bielefeld.de/fgweb/Preprints/fg03022.pdf","raw_type":"text"},{"id":"pmh:oai:pub.uni-bielefeld.de:1607379","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/1607379","pdf_url":null,"source":{"id":"https://openalex.org/S4306401671","display_name":"PUB \u2013 Publications at Bielefeld University (Bielefeld University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Beyn W-J, Th\u00fcmmler V. Freezing solutions of equivariant evolution equations. &lt;em&gt;SIAM Journal on Applied Dynamical Systems&lt;/em&gt;. 2004;3(2):85-116.","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1481457519","https://openalex.org/W1510014639","https://openalex.org/W1530314303","https://openalex.org/W1560060148","https://openalex.org/W1592421646","https://openalex.org/W1971808848","https://openalex.org/W1978221306","https://openalex.org/W1982293853","https://openalex.org/W1989896994","https://openalex.org/W1995504856","https://openalex.org/W2002341160","https://openalex.org/W2010435048","https://openalex.org/W2021243608","https://openalex.org/W2021280511","https://openalex.org/W2021369835","https://openalex.org/W2036280635","https://openalex.org/W2057743846","https://openalex.org/W2068665487","https://openalex.org/W2078570074","https://openalex.org/W2089259611","https://openalex.org/W2089286603","https://openalex.org/W2122591635","https://openalex.org/W2134778843","https://openalex.org/W2136645762","https://openalex.org/W2162356158","https://openalex.org/W2163036037","https://openalex.org/W2170733390","https://openalex.org/W4206763583","https://openalex.org/W4255777804"],"related_works":["https://openalex.org/W3148895720","https://openalex.org/W2393913406","https://openalex.org/W30258475","https://openalex.org/W2356579025","https://openalex.org/W2041926611","https://openalex.org/W1652778962","https://openalex.org/W4287818258","https://openalex.org/W3014434491","https://openalex.org/W4294109451","https://openalex.org/W3114474797"],"abstract_inverted_index":{"In":[0,73],"this":[1],"paper":[2],"we":[3,76],"develop":[4],"numerical":[5,145],"methods":[6,160],"for":[7],"integrating":[8],"general":[9],"evolution":[10],"equations":[11,49],"u":[12],"t":[13],"=":[14],"F(u),":[15],"$u(0)=u":[16],"0,":[17],"where":[18],"F":[19],"is":[20,33,123,139],"defined":[21],"on":[22,55],"a":[23,41,82,88,93,112,151],"dense":[24],"subspace":[25],"of":[26,40,64,70,84,87,114,121,128],"some":[27],"Banach":[28,99],"space":[29,185],"(generally":[30],"infinite-dimensional)":[31],"and":[32,163,183],"equivariant":[34],"with":[35,92,154],"respect":[36],"to":[37,150,171],"the":[38,62,65,78,85,97,103,119,126,129],"action":[39,63,86],"finite-dimensional":[42],"(not":[43],"necessarily":[44],"compact)":[45],"Lie":[46,130],"group.":[47,131],"Such":[48],"typically":[50],"arise":[51],"from":[52],"autonomous":[53],"PDEs":[54],"unbounded":[56],"domains":[57],"that":[58,174],"are":[59],"invariant":[60],"under":[61],"Euclidean":[66],"group":[67,90],"or":[68,178],"one":[69,182],"its":[71],"subgroups.":[72],"our":[74],"approach":[75],"write":[77],"solution":[79,105],"u(t)":[80],"as":[81,106,108,148],"composition":[83],"time-dependent":[89],"element":[91],"\"frozen":[94],"solution\"":[95],"in":[96,161,166,181],"given":[98,124],"space.":[100,167],"We":[101,168],"keep":[102],"frozen":[104],"constant":[107],"possible":[109],"by":[110,125,142],"introducing":[111],"set":[113],"algebraic":[115,137],"constraints":[116],"(phase":[117],"conditions),":[118],"number":[120],"which":[122],"dimension":[127],"The":[132],"resulting":[133],"PDAE":[134],"(partial":[135],"differential":[136],"equation)":[138],"then":[140],"solved":[141],"combining":[143],"classical":[144],"methods,":[146],"such":[147],"restriction":[149],"bounded":[152],"domain":[153],"asymptotic":[155],"boundary":[156],"conditions,":[157],"half-explicit":[158],"Euler":[159],"time,":[162],"finite":[164],"differences":[165],"provide":[169],"applications":[170],"reaction-diffusion":[172],"systems":[173],"have":[175],"traveling":[176],"wave":[177],"spiral":[179],"solutions":[180],"two":[184],"dimensions.":[186]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":6}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
