{"id":"https://openalex.org/W2045140942","doi":"https://doi.org/10.1016/s0893-9659(03)00080-6","title":"The energy space and norm growth for abstract wave equations","display_name":"The energy space and norm growth for abstract wave equations","publication_year":2003,"publication_date":"2003-07-01","ids":{"openalex":"https://openalex.org/W2045140942","doi":"https://doi.org/10.1016/s0893-9659(03)00080-6","mag":"2045140942"},"language":"en","primary_location":{"id":"doi:10.1016/s0893-9659(03)00080-6","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0893-9659(03)00080-6","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0893965903000806/pdf","source":{"id":"https://openalex.org/S7571225","display_name":"Applied Mathematics Letters","issn_l":"0893-9659","issn":["0893-9659","1873-5452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.sciencedirect.com/science/article/pii/S0893965903000806/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109396278","display_name":"Jerome A. Goldstein","orcid":null},"institutions":[{"id":"https://openalex.org/I94658018","display_name":"University of Memphis","ror":"https://ror.org/01cq23130","country_code":"US","type":"education","lineage":["https://openalex.org/I94658018"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J.A Goldstein","raw_affiliation_strings":["Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A","Department of Mathematical Sciences , University of Memphis , Memphis , TN 38152 , U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A","institution_ids":["https://openalex.org/I94658018"]},{"raw_affiliation_string":"Department of Mathematical Sciences , University of Memphis , Memphis , TN 38152 , U.S.A","institution_ids":["https://openalex.org/I94658018"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054757705","display_name":"Matthias G. Wacker","orcid":"https://orcid.org/0000-0002-2789-6463"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"M Wacker","raw_affiliation_strings":["Mathematisches Institut Auf der Morgenstelle 10 72076 T\u00fcbingen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut Auf der Morgenstelle 10 72076 T\u00fcbingen, Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054757705","https://openalex.org/A5109396278"],"corresponding_institution_ids":["https://openalex.org/I94658018"],"apc_list":{"value":3540,"currency":"USD","value_usd":3540},"apc_paid":null,"fwci":0.7787,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.66629526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"16","issue":"5","first_page":"767","last_page":"772"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9998999834060669,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9983999729156494,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9979000091552734,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8619381189346313},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.7179994583129883},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6975775361061096},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6515982151031494},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6371077299118042},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5585546493530273},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4805760383605957},{"id":"https://openalex.org/keywords/dalembert-operator","display_name":"D'Alembert operator","score":0.4633280634880066},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.46290501952171326},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4389648735523224},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.061664849519729614}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8619381189346313},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.7179994583129883},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6975775361061096},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6515982151031494},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6371077299118042},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5585546493530273},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4805760383605957},{"id":"https://openalex.org/C58677928","wikidata":"https://www.wikidata.org/wiki/Q911268","display_name":"D'Alembert operator","level":2,"score":0.4633280634880066},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46290501952171326},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4389648735523224},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.061664849519729614},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0893-9659(03)00080-6","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0893-9659(03)00080-6","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0893965903000806/pdf","source":{"id":"https://openalex.org/S7571225","display_name":"Applied Mathematics Letters","issn_l":"0893-9659","issn":["0893-9659","1873-5452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics Letters","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s0893-9659(03)00080-6","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0893-9659(03)00080-6","pdf_url":"https://www.sciencedirect.com/science/article/pii/S0893965903000806/pdf","source":{"id":"https://openalex.org/S7571225","display_name":"Applied Mathematics Letters","issn_l":"0893-9659","issn":["0893-9659","1873-5452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics Letters","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8799999952316284,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2045140942.pdf","grobid_xml":"https://content.openalex.org/works/W2045140942.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W71469676","https://openalex.org/W599293027","https://openalex.org/W1516587486","https://openalex.org/W1575147392","https://openalex.org/W2327908882","https://openalex.org/W4251761138","https://openalex.org/W6602946768"],"related_works":["https://openalex.org/W4280529579","https://openalex.org/W1992473810","https://openalex.org/W2950065126","https://openalex.org/W2393780731","https://openalex.org/W2964065719","https://openalex.org/W3090660127","https://openalex.org/W2045140942","https://openalex.org/W4246788756","https://openalex.org/W4300705797","https://openalex.org/W2088744976"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-02T14:50:37.381335","created_date":"2025-10-10T00:00:00"}
