{"id":"https://openalex.org/W2973106983","doi":"https://doi.org/10.3934/mcrf.2021044","title":"Asymptotic gain results for attractors of semilinear systems","display_name":"Asymptotic gain results for attractors of semilinear systems","publication_year":2021,"publication_date":"2021-09-08","ids":{"openalex":"https://openalex.org/W2973106983","doi":"https://doi.org/10.3934/mcrf.2021044","mag":"2973106983"},"language":"en","primary_location":{"id":"doi:10.3934/mcrf.2021044","doi":"https://doi.org/10.3934/mcrf.2021044","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mcrf.2021044","pdf_url":null,"source":{"id":"https://openalex.org/S2492071052","display_name":"Mathematical Control and Related Fields","issn_l":"2156-8499","issn":["2156-8499","2156-8472"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Control and Related Fields","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2973106983"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/mcrf.2021044","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010306970","display_name":"Jochen Schmid","orcid":"https://orcid.org/0000-0001-6527-537X","observed_orcids":["https://orcid.org/0000-0001-6527-537X"]},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]},{"id":"https://openalex.org/I4923324","display_name":"Fraunhofer-Gesellschaft","ror":"https://ror.org/05hkkdn48","country_code":"DE","type":"government","lineage":["https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Jochen Schmid","raw_affiliation_strings":["Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany","Fraunhofer Society"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Industrial Mathematics (ITWM), Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany","institution_ids":["https://openalex.org/I3019415892"]},{"raw_affiliation_string":"Fraunhofer Society","institution_ids":["https://openalex.org/I4923324"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077777063","display_name":"Oleksiy V. Kapustyan","orcid":"https://orcid.org/0000-0002-9373-6812","observed_orcids":["https://orcid.org/0000-0002-9373-6812"]},"institutions":[{"id":"https://openalex.org/I189238007","display_name":"Taras Shevchenko National University of Kyiv","ror":"https://ror.org/02aaqv166","country_code":"UA","type":"education","lineage":["https://openalex.org/I189238007"]},{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE","UA"],"is_corresponding":false,"raw_author_name":"Oleksiy Kapustyan","raw_affiliation_strings":["Institute for Mathematics, University of W\u00fcrzburg, 97074 W\u00fcrzburg, Germany","Kiev National Taras Shevchenko University, 01033 Kiev, Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematics, University of W\u00fcrzburg, 97074 W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]},{"raw_affiliation_string":"Kiev National Taras Shevchenko University, 01033 Kiev, Ukraine","institution_ids":["https://openalex.org/I189238007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004635071","display_name":"Sergey N. Dashkovskiy","orcid":"https://orcid.org/0000-0001-7049-012X","observed_orcids":["https://orcid.org/0000-0001-7049-012X"]},"institutions":[{"id":"https://openalex.org/I189238007","display_name":"Taras Shevchenko National University of Kyiv","ror":"https://ror.org/02aaqv166","country_code":"UA","type":"education","lineage":["https://openalex.org/I189238007"]},{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE","UA"],"is_corresponding":false,"raw_author_name":"Sergey Dashkovskiy","raw_affiliation_strings":["Institute for Mathematics, University of W\u00fcrzburg, 97074 W\u00fcrzburg, Germany","Kiev National Taras Shevchenko University, 01033 Kiev, Ukraine","University of Wurzburg#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematics, University of W\u00fcrzburg, 97074 W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]},{"raw_affiliation_string":"Kiev National Taras Shevchenko University, 01033 Kiev, Ukraine","institution_ids":["https://openalex.org/I189238007"]},{"raw_affiliation_string":"University of Wurzburg#TAB#","institution_ids":["https://openalex.org/I25974101"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5010306970"],"corresponding_institution_ids":["https://openalex.org/I3019415892","https://openalex.org/I4923324"],"apc_list":null,"apc_paid":null,"fwci":1.1282,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.73679451,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"12","issue":"3","first_page":"763","last_page":"763"},"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":0.9990000128746033,"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":0.9990000128746033,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.00039999998989515007,"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"}},{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/input-to-state-practical-stability","display_name":"input-to-state practical stability","score":0.8659999966621399},{"id":"https://openalex.org/keywords/semilinear-systems","display_name":"semilinear systems","score":0.9139999747276306},{"id":"https://openalex.org/keywords/global-attractor","display_name":"global attractor","score":0.8759999871253967},{"id":"https://openalex.org/keywords/nonlinear-reaction-diffusion-equations","display_name":"nonlinear reaction-diffusion equations","score":0.925000011920929},{"id":"https://openalex.org/keywords/asymptotic-controllability","display_name":"asymptotic controllability","score":0.5809999704360962}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.9299893379211426},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6702917814254761},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6476743817329407},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.6403795480728149},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5904014706611633},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5402611494064331},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.5297026634216309},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5175111293792725},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38189470767974854},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.33602672815322876},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2390504777431488},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1865328550338745},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0755966305732727},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.04856032133102417},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3934/mcrf.2021044","doi":"https://doi.org/10.3934/mcrf.2021044","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mcrf.2021044","pdf_url":null,"source":{"id":"https://openalex.org/S2492071052","display_name":"Mathematical Control and Related Fields","issn_l":"2156-8499","issn":["2156-8499","2156-8472"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Control and Related Fields","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1909.06302","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.06302","pdf_url":"https://arxiv.org/pdf/1909.06302","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":"pmh:oai:fraunhofer.de:N-642257","doi":null,"is_oa":true,"landing_page_url":"http://publica.fraunhofer.de/documents/N-642257.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400801","display_name":"Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fraunhofer ITWM","raw_type":"article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/414319","doi":null,"is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/414319","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"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":"paper"},{"id":"pmh:oai:publica.fraunhofer.de:publica/427466","doi":null,"is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/427466","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"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":"journal article"},{"id":"doi:10.48550/arxiv.1909.06302","doi":"https://doi.org/10.48550/arxiv.1909.06302","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.06302","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":"doi:10.3934/mcrf.2021044","doi":"https://doi.org/10.3934/mcrf.2021044","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mcrf.2021044","pdf_url":null,"source":{"id":"https://openalex.org/S2492071052","display_name":"Mathematical Control and Related Fields","issn_l":"2156-8499","issn":["2156-8499","2156-8472"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Control and Related Fields","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3375019125","display_name":null,"funder_award_id":"DA 767/12\u20101","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320325308","display_name":"State Fund for Fundamental Research of Ukraine","ror":"https://ror.org/05k0zzt52"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2973106983.pdf","grobid_xml":"https://content.openalex.org/works/W2973106983.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W76426481","https://openalex.org/W203646022","https://openalex.org/W1527296550","https://openalex.org/W1594759473","https://openalex.org/W1606157354","https://openalex.org/W1984507032","https://openalex.org/W1991014733","https://openalex.org/W2015057328","https://openalex.org/W2022806724","https://openalex.org/W2029950695","https://openalex.org/W2057820893","https://openalex.org/W2065060801","https://openalex.org/W2092180670","https://openalex.org/W2134078068","https://openalex.org/W2135897334","https://openalex.org/W2151136609","https://openalex.org/W2247036405","https://openalex.org/W2347136120","https://openalex.org/W2382263266","https://openalex.org/W2529352710","https://openalex.org/W2548079377","https://openalex.org/W2583096043","https://openalex.org/W2600536581","https://openalex.org/W2601514544","https://openalex.org/W2605644331","https://openalex.org/W2630013275","https://openalex.org/W2766268847","https://openalex.org/W2767007456","https://openalex.org/W2776041833","https://openalex.org/W2799010584","https://openalex.org/W2884117905","https://openalex.org/W2900589485","https://openalex.org/W2901683690","https://openalex.org/W2940525678","https://openalex.org/W2962862651","https://openalex.org/W2969813910","https://openalex.org/W2972999908","https://openalex.org/W2977385926","https://openalex.org/W2996307774","https://openalex.org/W3029891775","https://openalex.org/W3104949460","https://openalex.org/W3119684003","https://openalex.org/W3142080596","https://openalex.org/W3154893660","https://openalex.org/W4244149884","https://openalex.org/W4245807314","https://openalex.org/W4300857049","https://openalex.org/W6929472556"],"related_works":["https://openalex.org/W3154893660","https://openalex.org/W2972999908","https://openalex.org/W3207002422","https://openalex.org/W4368368681","https://openalex.org/W4322580358","https://openalex.org/W4411218576","https://openalex.org/W1565776550","https://openalex.org/W4313317372"],"abstract_inverted_index":{"We":[0,23],"establish":[1],"asymptotic":[2],"gain":[3],"along":[4],"with":[5],"input-to-state":[6],"practical":[7],"stability":[8],"results":[9,26],"for":[10,39],"disturbed":[11,36],"semilinear":[12],"systems":[13],"w.r.t.":[14],"the":[15,19],"global":[16],"attractor":[17],"of":[18,31],"respective":[20],"undisturbed":[21],"system.":[22],"apply":[24],"our":[25],"to":[27],"a":[28],"large":[29],"class":[30],"nonlinear":[32],"reaction-diffusion":[33],"equations":[34],"comprising":[35],"Chaffee\u2013Infante":[37],"equations,":[38],"example.":[40]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2019-09-19T00:00:00"}
