{"id":"https://openalex.org/W4385698124","doi":"https://doi.org/10.1201/9781003499152-21","title":"Linear Partial Differential Equations with Delay","display_name":"Linear Partial Differential Equations with Delay","publication_year":2023,"publication_date":"2023-08-09","ids":{"openalex":"https://openalex.org/W4385698124","doi":"https://doi.org/10.1201/9781003499152-21"},"language":"en","primary_location":{"id":"doi:10.1201/9781003499152-21","doi":"https://doi.org/10.1201/9781003499152-21","is_oa":false,"landing_page_url":"https://doi.org/10.1201/9781003499152-21","pdf_url":null,"source":{"id":"https://openalex.org/S4306467597","display_name":"Chapman & Hall/CRC eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320449","host_organization_name":"Informa","host_organization_lineage":["https://openalex.org/P4310320449"],"host_organization_lineage_names":["Informa"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Handbook of Linear Partial Differential Equations for Engineers and Scientists","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W120308165","display_name":"Handbook of Linear Partial Differential Equations for Engineers and Scientists"},"type":"book-chapter","is_traditional":true,"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/A5077379445","display_name":"Andrei D. Polyanin","orcid":"https://orcid.org/0000-0002-2610-0590","observed_orcids":["https://orcid.org/0000-0002-2610-0590"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrei D. Polyanin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040356398","display_name":"Vsevolod G. Sorokin","orcid":"https://orcid.org/0000-0002-9687-7856","observed_orcids":["https://orcid.org/0000-0002-9687-7856"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vsevolod G. Sorokin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5031651904","display_name":"Alexei I. Zhurov","orcid":"https://orcid.org/0000-0002-5594-0740","observed_orcids":["https://orcid.org/0000-0002-5594-0740"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexei I. Zhurov","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":1.636,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.82632794,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1019","last_page":"1066"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9970999956130981,"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"}},"topics":[{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9970999956130981,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.0019000000320374966,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.0006000000284984708,"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/separable-solutions","display_name":"separable solutions","score":0.8090000152587891},{"id":"https://openalex.org/keywords/separation-of-variables","display_name":"separation of variables","score":0.8980000019073486},{"id":"https://openalex.org/keywords/integral-transforms","display_name":"integral transforms","score":0.7950000166893005},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equations","display_name":"parabolic equations","score":0.7549999952316284},{"id":"https://openalex.org/keywords/hyperbolic-equations","display_name":"hyperbolic equations","score":1.0},{"id":"https://openalex.org/keywords/initial-boundary-value-problem","display_name":"initial-boundary value problem","score":0.8840000033378601},{"id":"https://openalex.org/keywords/boundary-conditions","display_name":"boundary conditions","score":0.7179999947547913},{"id":"https://openalex.org/keywords/constant-delay","display_name":"constant delay","score":0.6700000166893005}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4865235686302185},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43513017892837524},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41017842292785645}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1201/9781003499152-21","doi":"https://doi.org/10.1201/9781003499152-21","is_oa":false,"landing_page_url":"https://doi.org/10.1201/9781003499152-21","pdf_url":null,"source":{"id":"https://openalex.org/S4306467597","display_name":"Chapman & Hall/CRC eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320449","host_organization_name":"Informa","host_organization_lineage":["https://openalex.org/P4310320449"],"host_organization_lineage_names":["Informa"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Handbook of Linear Partial Differential Equations for Engineers and Scientists","raw_type":"book-chapter"},{"id":"doi:10.1201/9781003042310-2","doi":"https://doi.org/10.1201/9781003042310-2","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1201/9781003042310-2","pdf_url":null,"source":{"id":"https://openalex.org/S4306467597","display_name":"Chapman & Hall/CRC eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320449","host_organization_name":"Informa","host_organization_lineage":["https://openalex.org/P4310320449"],"host_organization_lineage_names":["Informa"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Delay Ordinary and Partial Differential Equations","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4401108575","https://openalex.org/W2157346442","https://openalex.org/W7151813025","https://openalex.org/W4385697988","https://openalex.org/W2072569472","https://openalex.org/W2060415155","https://openalex.org/W2058783395","https://openalex.org/W7167691169","https://openalex.org/W2078188679","https://openalex.org/W1986754982"],"abstract_inverted_index":{"Second-order":[0],"linear":[1,23,52,72,143],"partial":[2,25,73,84,96,110,119,144],"differential":[3,26,54,74,85,97,111,120,145],"equations":[4,27,55,75,86,98,112,121,146],"of":[5,37,51,71,82,129,133],"the":[6,18,35,105,137],"parabolic":[7],"or":[8,39,131],"hyperbolic":[9],"type":[10],"with":[11,56,76,99,122],"constant":[12,62],"delay":[13,63,77,100,123],"are":[14,78,101],"not":[15],"uncommon":[16],"in":[17,91,103,136],"literature":[19],"and":[20,60],"applications.":[21],"Many":[22,69],"homogeneous":[24,53],"have":[28],"solutions":[29],"that":[30,64],"can":[31,124],"be":[32,125],"represented":[33],"as":[34,108,140],"product":[36],"two":[38],"more":[40],"functions":[41],"dependent":[42],"on":[43],"different":[44],"arguments.":[45],"This":[46],"chapter":[47],"lists":[48],"frequent":[49],"types":[50],"several":[57],"independent":[58],"variables":[59,130],"a":[61],"admit":[65],"exact":[66],"separable":[67],"solutions.":[68],"properties":[70],"similar":[79],"to":[80],"those":[81,141],"respective":[83],"without":[87,113,147],"delay.":[88,114,148],"Boundary":[89],"conditions":[90],"initial-boundary":[92],"value":[93],"problems":[94,116],"for":[95,109,142],"stated":[102],"exactly":[104],"same":[106,138],"way":[107],"Linear":[115],"described":[117],"by":[118],"solved":[126],"using":[127],"separation":[128],"methods":[132],"integral":[134],"transforms":[135],"ways":[139]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2023-08-10T00:00:00"}