{"id":"https://openalex.org/W2236944626","doi":"https://doi.org/10.1137/15m101525x","title":"The Generalized Diffusion Phenomenon and Applications","display_name":"The Generalized Diffusion Phenomenon and Applications","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2236944626","doi":"https://doi.org/10.1137/15m101525x","mag":"2236944626"},"language":"en","primary_location":{"id":"doi:10.1137/15m101525x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m101525x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","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/A5054047964","display_name":"Petronela Radu","orcid":"https://orcid.org/0000-0001-8628-2771"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Petronela Radu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110632413","display_name":"Grozdena Todorova","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Grozdena Todorova","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5084789698","display_name":"Borislav Yordanov","orcid":"https://orcid.org/0000-0003-0658-1750"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Borislav Yordanov","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":5.4354,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.95832211,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"48","issue":"1","first_page":"174","last_page":"203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9994999766349792,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9994999766349792,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9994000196456909,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8253418803215027},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.8099467158317566},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.6943439245223999},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6011200547218323},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5842936038970947},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5108465552330017},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.501082181930542},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.45093050599098206},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4144194722175598},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.105703204870224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8253418803215027},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.8099467158317566},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.6943439245223999},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6011200547218323},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5842936038970947},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5108465552330017},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.501082181930542},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.45093050599098206},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4144194722175598},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.105703204870224},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m101525x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m101525x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W216257128","https://openalex.org/W644710670","https://openalex.org/W651321014","https://openalex.org/W1482591152","https://openalex.org/W1486079966","https://openalex.org/W1492498476","https://openalex.org/W1528671428","https://openalex.org/W1550032733","https://openalex.org/W1555315878","https://openalex.org/W1612577201","https://openalex.org/W1799652015","https://openalex.org/W1968020927","https://openalex.org/W1968834064","https://openalex.org/W1971657246","https://openalex.org/W1971779315","https://openalex.org/W1973127220","https://openalex.org/W1975105209","https://openalex.org/W1977309464","https://openalex.org/W1985006985","https://openalex.org/W1996054514","https://openalex.org/W2000476216","https://openalex.org/W2002507095","https://openalex.org/W2006354315","https://openalex.org/W2008115607","https://openalex.org/W2009787868","https://openalex.org/W2011317157","https://openalex.org/W2011540258","https://openalex.org/W2012828992","https://openalex.org/W2019248995","https://openalex.org/W2023102307","https://openalex.org/W2028547893","https://openalex.org/W2033841814","https://openalex.org/W2035286570","https://openalex.org/W2035731630","https://openalex.org/W2039787685","https://openalex.org/W2040402168","https://openalex.org/W2044309359","https://openalex.org/W2048627180","https://openalex.org/W2048695003","https://openalex.org/W2048877476","https://openalex.org/W2051917048","https://openalex.org/W2060945009","https://openalex.org/W2064447648","https://openalex.org/W2069887814","https://openalex.org/W2072177051","https://openalex.org/W2074718504","https://openalex.org/W2081333005","https://openalex.org/W2087757234","https://openalex.org/W2091018235","https://openalex.org/W2091741254","https://openalex.org/W2094739145","https://openalex.org/W2119414533","https://openalex.org/W2319221982","https://openalex.org/W2487777714","https://openalex.org/W2924607668","https://openalex.org/W2928381655","https://openalex.org/W3217568251","https://openalex.org/W4213378375"],"related_works":["https://openalex.org/W2946733187","https://openalex.org/W1606423697","https://openalex.org/W2064533477","https://openalex.org/W2048604961","https://openalex.org/W4249099142","https://openalex.org/W2327789793","https://openalex.org/W4233447357","https://openalex.org/W1988511271","https://openalex.org/W1982474834","https://openalex.org/W1993685989"],"abstract_inverted_index":{"We":[0,68],"study":[1],"the":[2,25,45,49,62,89,94,104],"asymptotic":[3],"behavior":[4],"of":[5,33,38],"solutions":[6,32,37],"to":[7],"dissipative":[8,78],"wave":[9,100],"equations":[10,35,40,80,101],"involving":[11],"two":[12],"noncommuting":[13],"self-adjoint":[14],"operators":[15],"in":[16],"a":[17,54],"Hilbert":[18],"space.":[19],"The":[20],"main":[21],"result":[22],"is":[23],"that":[24],"abstract":[26],"diffusion":[27,39,46,64],"phenomenon":[28],"takes":[29],"place.":[30],"Thus":[31],"such":[34],"approach":[36],"at":[41],"large":[42],"times.":[43],"When":[44],"semigroup":[47],"has":[48],"Markov":[50],"property":[51],"and":[52,66],"satisfies":[53],"Nash-type":[55],"inequality,":[56],"we":[57,92],"obtain":[58,93],"precise":[59],"estimates":[60,76,97],"for":[61,77,98],"consecutive":[63],"approximations":[65],"remainders.":[67],"present":[69],"several":[70],"important":[71],"applications":[72],"including":[73],"sharp":[74],"decay":[75,96,105],"hyperbolic":[79],"with":[81,102],"variable":[82],"coefficients":[83],"on":[84],"an":[85],"exterior":[86],"domain.":[87],"In":[88],"nonlocal":[90,99],"case":[91],"first":[95],"damping;":[103],"rates":[106],"are":[107],"sharp.":[108]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}