{"id":"https://openalex.org/W1996741937","doi":"https://doi.org/10.1137/s003614109833793x","title":"Stability and Hopf Bifurcation for Fully Nonlinear Parabolic-Hyperbolic Equations","display_name":"Stability and Hopf Bifurcation for Fully Nonlinear Parabolic-Hyperbolic Equations","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1996741937","doi":"https://doi.org/10.1137/s003614109833793x","mag":"1996741937"},"language":"en","primary_location":{"id":"doi:10.1137/s003614109833793x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614109833793x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5087100672","display_name":"Herbert Koch","orcid":"https://orcid.org/0000-0001-6736-1378"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Herbert Koch","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045570271","display_name":"Stuart S. Antman","orcid":"https://orcid.org/0000-0001-6135-8848"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stuart S. Antman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.992,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.897252,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"32","issue":"2","first_page":"360","last_page":"384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998000264167786,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9919999837875366,"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"}},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9855999946594238,"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":0.9016460180282593},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6509811878204346},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5399167537689209},{"id":"https://openalex.org/keywords/stable-manifold","display_name":"Stable manifold","score":0.5094817280769348},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.48661932349205017},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.48598775267601013},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.4754699766635895},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.430631548166275},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.42133277654647827},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4205210506916046},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.41042786836624146},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.3271692991256714},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.31241753697395325}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9016460180282593},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6509811878204346},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5399167537689209},{"id":"https://openalex.org/C50429861","wikidata":"https://www.wikidata.org/wiki/Q3554830","display_name":"Stable manifold","level":2,"score":0.5094817280769348},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.48661932349205017},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.48598775267601013},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.4754699766635895},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.430631548166275},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.42133277654647827},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4205210506916046},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.41042786836624146},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.3271692991256714},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.31241753697395325},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s003614109833793x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614109833793x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.29.6800","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.6800","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.sfb359.uni-heidelberg.de/PP/Preprint1998-14.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1508861003","https://openalex.org/W1538929409","https://openalex.org/W1560060148","https://openalex.org/W1602967628","https://openalex.org/W1886021430","https://openalex.org/W1980995521","https://openalex.org/W1992077739","https://openalex.org/W2001960927","https://openalex.org/W2008100206","https://openalex.org/W2021089528","https://openalex.org/W2035695789","https://openalex.org/W2073370369","https://openalex.org/W2082198150","https://openalex.org/W2082734651","https://openalex.org/W2084487345","https://openalex.org/W2089876099","https://openalex.org/W2090896589","https://openalex.org/W2330325083","https://openalex.org/W2330668771","https://openalex.org/W4243738351","https://openalex.org/W4302061159"],"related_works":["https://openalex.org/W1940963234","https://openalex.org/W2095404847","https://openalex.org/W2069807835","https://openalex.org/W2077191083","https://openalex.org/W2034258422","https://openalex.org/W2044253876","https://openalex.org/W2695807795","https://openalex.org/W2025732048","https://openalex.org/W1970195792","https://openalex.org/W1996741937"],"abstract_inverted_index":{"We":[0],"develop":[1],"the":[2,30,33,38,53,61,64,67,73,77],"principle":[3],"of":[4,14,32,63,66,79,82,85,88,117,121,126],"linearized":[5,68],"stability":[6],"and":[7,59,97,130],"a":[8,15,43,80,118,134],"Hopf":[9],"bifurcation":[10],"theorem":[11],"as":[12],"elements":[13],"geometric":[16],"theory":[17],"for":[18,76],"fully":[19],"nonlinear":[20],"parabolic-hyperbolic":[21],"problems.":[22],"Crucial":[23],"steps":[24],"in":[25,133],"our":[26],"work":[27],"are":[28,110],"showing":[29,36],"differentiability":[31],"time-t":[34],"map,":[35],"that":[37,93,123],"admissible":[39],"initial":[40],"data":[41],"form":[42],"manifold":[44],"(whose":[45],"failure":[46],"to":[47,52],"be":[48],"linear":[49],"is":[50],"due":[51],"general":[54],"boundary":[55],"conditions":[56],"we":[57],"study),":[58],"analyzing":[60],"spectrum":[62],"generator":[65],"semigroup.":[69],"This":[70],"paper":[71],"provides":[72],"abstract":[74],"framework":[75],"study":[78],"class":[81],"concrete":[83],"problems":[84],"self-sustained":[86],"oscillations":[87],"nonlinearly":[89],"viscoelastic":[90],"bodies":[91],"like":[92],"treated":[94],"by":[95],"Antman":[96],"Koch":[98],"[t":[99],"SIAM":[100],"J.":[101],"Appl.":[102],"Math.,":[103],"60":[104],"(2000),":[105],"pp.":[106],"1357--1387].":[107],"Our":[108],"equations":[109,129,132],"intrinsically":[111],"interesting:":[112],"They":[113],"provide":[114],"an":[115],"example":[116],"new":[119],"kind":[120],"semiflow":[122],"combines":[124],"properties":[125],"ordinary":[127],"differential":[128],"parabolic":[131],"novel":[135],"way.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
