{"doi":"10.1007/978-3-030-15096-9_6","title":"On Optimal Decay Estimates for ODEs and PDEs with Modal Decomposition","abstract":null,"journal":"Springer Proceedings in Mathematics & Statistics","year":2019,"id":20843,"datarank":0.3453877639491069,"base_score":2.302585092994046,"endowment":2.302585092994046,"self_citation_contribution":0.3453877639491069,"citation_network_contribution":0.0,"self_endowment_contribution":0.3453877639491069,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":9,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":1,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":136417,"name":"Anton Arnold","orcid":null,"position":1,"is_corresponding":false},{"id":136418,"name":"Beatrice Signorello","orcid":null,"position":2,"is_corresponding":false},{"id":136416,"name":"Franz Achleitner","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":0.6931471805599453,"endowment":0.6931471805599453,"datacite_reuse_total":1,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"21071399","pmcid":null,"openalex_id":"https://openalex.org/W2787383220","authors":[],"funders":[{"funder_name":"Austrian Science Fund (FWF)","grant_id":"W 1245","title":"Dissipation and dispersion in differential equations"}],"total_grants":1,"fwci":0.6934,"citation_percentile":0.56216713,"influential_citations":0,"citation_trend":[{"year":2022,"count":1}],"oa_status":"green","license":"Springer TDM","oa_locations":[{"url":"https://arxiv.org/pdf/1802.00767","host_type":"repository"},{"url":"https://arxiv.org/pdf/1802.00767","host_type":"GREEN"},{"url":"https://arxiv.org/pdf/1802.00767","host_type":"repository"},{"url":"http://link.springer.com/content/pdf/10.1007/978-3-030-15096-9_6","host_type":"publisher"},{"url":"http://arxiv.org/abs/1802.00767","host_type":"repository"},{"url":"https://doi.org/10.1007/978-3-030-15096-9_6","host_type":"book series"},{"url":"https://arxiv.org/pdf/1802.00767.pdf","host_type":"repository"},{"url":"https://doi.org/10.48550/arxiv.1802.00767","host_type":"repository"},{"url":"http://arxiv.org/pdf/1802.00767","host_type":""},{"url":"https://dx.doi.org/10.48550/arxiv.1802.00767","host_type":""},{"url":"https://dx.doi.org/10.1007/978-3-030-15096-9_6","host_type":""}],"fields_of_study":["Stability and Controllability of Differential Equations","Numerical methods for differential equations","Nonlinear Differential Equations Analysis","Mathematics","0101 mathematics","01 natural sciences"],"mesh_terms":[],"keywords":["Ode","Mathematics","Lyapunov function","Applied mathematics","Exponential decay","Semigroup","Constant (computer programming)","Multiplicative function","Ordinary differential equation","Diagonalizable matrix","Rate of convergence","Mathematical analysis","Nonlinear system","Differential equation","Eigenvalues and eigenvectors","Computer science","Physics","Symmetric matrix","Mathematics - Analysis of PDEs","35Q82, 35B40, 34D05, 37B25","FOS: Mathematics","Analysis of PDEs (math.AP)"],"sdg_mappings":[],"linked_datasets":[{"doi":"10.48550/arxiv.1802.00767","title":"On optimal decay estimates for ODEs and PDEs with modal decomposition","publisher":"arXiv","resource_type":"Text"}],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-06T12:24:34.086474Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}