{"id":"https://openalex.org/W7214290565","doi":"https://doi.org/10.48550/arxiv.2609.29778","title":"Global Well-Posedness and Asymptotic Behavior of Energy-Damped Subquintic Wave Equations","display_name":"Global Well-Posedness and Asymptotic Behavior of Energy-Damped Subquintic Wave Equations","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214290565","doi":"https://doi.org/10.48550/arxiv.2609.29778"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.29778","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29778","pdf_url":"https://arxiv.org/pdf/2609.29778","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.29778","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053756814","display_name":"Irena Lasiecka","orcid":"https://orcid.org/0000-0003-3342-2202","observed_orcids":["https://orcid.org/0000-0003-3342-2202"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lasiecka, Irena","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152833114","display_name":"Yanan Li","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yanan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5038535756","display_name":"Vando Narciso","orcid":"https://orcid.org/0000-0003-4506-4879","observed_orcids":["https://orcid.org/0000-0003-4506-4879"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Narciso, Vando","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":1.0,"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":1.0,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.0,"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/wave-equation","display_name":"wave equation","score":0.7900000214576721},{"id":"https://openalex.org/keywords/damping","display_name":"damping","score":0.550000011920929},{"id":"https://openalex.org/keywords/nonlocal-damping","display_name":"nonlocal damping","score":0.8330000042915344},{"id":"https://openalex.org/keywords/global-existence","display_name":"global existence","score":0.7049999833106995},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6880000233650208},{"id":"https://openalex.org/keywords/bounded-domains","display_name":"bounded domains","score":0.800000011920929},{"id":"https://openalex.org/keywords/compact-global-attractor","display_name":"compact global attractor","score":0.8309999704360962},{"id":"https://openalex.org/keywords/kolmogorov-epsilon-entropy","display_name":"Kolmogorov epsilon-entropy","score":0.9610000252723694},{"id":"https://openalex.org/keywords/quasi-stability","display_name":"quasi-stability","score":0.9200000166893005},{"id":"https://openalex.org/keywords/finite-dimensionality","display_name":"finite dimensionality","score":0.5860000252723694},{"id":"https://openalex.org/keywords/exponential-attractors","display_name":"exponential attractors","score":0.902999997138977},{"id":"https://openalex.org/keywords/long-time-behavior","display_name":"long-time behavior","score":0.8479999899864197},{"id":"https://openalex.org/keywords/optics","display_name":"optics","score":0.49900001287460327}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7466999888420105},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.738099992275238},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6133999824523926},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.5972999930381775},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5849999785423279},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5555999875068665},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.5458999872207642},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5450000166893005},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.53329998254776},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5130000114440918},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4569999873638153},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.43309998512268066},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3903999924659729},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.366100013256073},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.36169999837875366},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.3361000120639801},{"id":"https://openalex.org/C180188523","wikidata":"https://www.wikidata.org/wiki/Q574576","display_name":"Exponential decay","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.29089999198913574},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.2736000120639801},{"id":"https://openalex.org/C2779844894","wikidata":"https://www.wikidata.org/wiki/Q5421516","display_name":"Exponential dichotomy","level":3,"score":0.26019999384880066},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.2540999948978424}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.29778","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29778","pdf_url":"https://arxiv.org/pdf/2609.29778","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2609.29778","doi":"https://doi.org/10.48550/arxiv.2609.29778","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.29778","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.29778","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29778","pdf_url":"https://arxiv.org/pdf/2609.29778","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1835701300","display_name":"Control of Fluid-Structure Interactions: Finite Dimensional Strategies for Flutter/Turbulence Suppression","funder_award_id":"2205508","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214290565.pdf","grobid_xml":"https://content.openalex.org/works/W7214290565.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1647231376","https://openalex.org/W7203927614","https://openalex.org/W1489183357","https://openalex.org/W4401760906","https://openalex.org/W4281613982","https://openalex.org/W4414171489","https://openalex.org/W3090544773","https://openalex.org/W1542326368","https://openalex.org/W4281616981","https://openalex.org/W2094710203"],"abstract_inverted_index":{"In":[0,105],"this":[1,144],"article,":[2],"we":[3,120],"consider":[4],"a":[5,9,14,26,92,115,169],"wave":[6,74],"equation":[7],"on":[8,21,59],"bounded":[10,60],"three-dimensional":[11,73],"domain,":[12],"featuring":[13],"degenerate":[15],"nonlocal":[16,76],"damping":[17,108],"mechanism":[18],"that":[19,81,111],"depends":[20],"the":[22,48,66,70,89,106,112,122,138,153,158],"system's":[23],"energy":[24],"and":[25,78,96,165,168],"source":[27],"term":[28],"with":[29,55],"subquintic":[30],"growth.":[31],"This":[32],"class":[33],"of":[34,91,126,152],"models":[35],"is":[36,69],"motivated":[37],"by":[38,51],"applications":[39],"in":[40,47,65,133],"optical":[41],"physics.":[42],"We":[43,87],"establish":[44,150],"global":[45,94,159],"existence":[46,90],"Shatah--Strichartz":[49],"sense":[50],"combining":[52],"Galerkin":[53],"approximations":[54],"space-time":[56],"Strichartz":[57,124],"estimates":[58,125],"domains.":[61],"A":[62],"central":[63],"difficulty":[64],"long-time":[67],"analysis":[68],"interplay":[71],"between":[72],"dynamics,":[75],"damping,":[77],"forcing":[79],"terms":[80],"are":[82],"not":[83],"locally":[84],"Lipschitz":[85],"continuous.":[86],"prove":[88],"compact":[93],"attractor":[95,160,172],"derive":[97],"an":[98],"upper":[99],"bound":[100],"for":[101],"its":[102],"Kolmogorov":[103],"$\\varepsilon$-entropy.":[104],"non-degenerate":[107],"case,":[109],"assuming":[110],"domain":[113],"has":[114,161],"smooth,":[116],"strictly":[117],"convex":[118],"boundary,":[119],"exploit":[121],"refined":[123],"Ivanovici":[127],"{\\it":[128],"et":[129],"al.}~\\cite{Ivanovici-Lascar-Lebeau-Planchon-2023},":[130],"which":[131],"yield,":[132],"particular,":[134],"$u\\in":[135],"L^3_tL^{18}_x$.":[136],"Under":[137],"further":[139],"assumption":[140],"$f\\in":[141],"C^2(\\mathbb":[142],"R)$,":[143],"improved":[145],"integrability":[146],"allows":[147],"us":[148],"to":[149],"quasi-stability":[151],"associated":[154],"dynamical":[155],"system.":[156],"Consequently,":[157],"finite":[162],"fractal":[163],"dimension":[164],"higher":[166],"regularity,":[167],"generalized":[170],"exponential":[171],"exists.":[173]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-26T00:00:00"}