{"id":"https://openalex.org/W2010556130","doi":"https://doi.org/10.1137/s0036139993269254","title":"Internal Layers, Small Eigenvalues, and the Sensitivity of Metastable Motion","display_name":"Internal Layers, Small Eigenvalues, and the Sensitivity of Metastable Motion","publication_year":1995,"publication_date":"1995-04-01","ids":{"openalex":"https://openalex.org/W2010556130","doi":"https://doi.org/10.1137/s0036139993269254","mag":"2010556130"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139993269254","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139993269254","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","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/A5037517718","display_name":"Michael J. Ward","orcid":"https://orcid.org/0000-0001-6959-7202"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael J. Ward","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110143740","display_name":"Luis G. Reyna","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luis G. Reyna","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":2.636,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.89011203,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"55","issue":"2","first_page":"425","last_page":"445"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9973000288009644,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9973000288009644,"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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6953691244125366},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.6762996912002563},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6731207370758057},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6437832117080688},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6243516802787781},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5314133763313293},{"id":"https://openalex.org/keywords/shock","display_name":"Shock (circulatory)","score":0.5045427083969116},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4883684515953064},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.47133708000183105},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.44844159483909607},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4182599186897278},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.24907907843589783},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24504125118255615}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6953691244125366},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.6762996912002563},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6731207370758057},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6437832117080688},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6243516802787781},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5314133763313293},{"id":"https://openalex.org/C2781300812","wikidata":"https://www.wikidata.org/wiki/Q178061","display_name":"Shock (circulatory)","level":2,"score":0.5045427083969116},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4883684515953064},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.47133708000183105},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.44844159483909607},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4182599186897278},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.24907907843589783},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24504125118255615},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","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/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139993269254","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139993269254","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","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":25,"referenced_works":["https://openalex.org/W40253171","https://openalex.org/W98728907","https://openalex.org/W1803017756","https://openalex.org/W2002248925","https://openalex.org/W2015539642","https://openalex.org/W2018555509","https://openalex.org/W2023530101","https://openalex.org/W2039195921","https://openalex.org/W2045755160","https://openalex.org/W2048738870","https://openalex.org/W2065676431","https://openalex.org/W2073316428","https://openalex.org/W2075151302","https://openalex.org/W2078851442","https://openalex.org/W2078877786","https://openalex.org/W2091379762","https://openalex.org/W2127116451","https://openalex.org/W2136919854","https://openalex.org/W2158207266","https://openalex.org/W2266022734","https://openalex.org/W2271012468","https://openalex.org/W2474406097","https://openalex.org/W2515590532","https://openalex.org/W3141151088","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1974935850","https://openalex.org/W2074350688","https://openalex.org/W3158981924","https://openalex.org/W2042589464","https://openalex.org/W4252883813","https://openalex.org/W2346128247","https://openalex.org/W2078650164","https://openalex.org/W2158562798","https://openalex.org/W3047214821","https://openalex.org/W2089283247"],"abstract_inverted_index":{"On":[0],"a":[1,19,37,63,77,90],"semi-infinite":[2,54,74],"domain,":[3],"an":[4],"analytical":[5,108],"characterization":[6],"of":[7,67,93,97,106],"exponentially":[8],"slow":[9,42,49],"internal":[10,120],"layer":[11,121],"motion":[12,43],"for":[13,18],"the":[14,48,53,73,94,98,107],"Allen\u2013Cahn":[15],"equation":[16],"and":[17,86],"singularly":[20],"perturbed":[21],"viscous":[22],"shock":[23],"problem":[24],"is":[25,89],"given.":[26],"The":[27],"results":[28,32,109],"extend":[29],"some":[30],"previous":[31],"that":[33,47],"were":[34],"restricted":[35],"to":[36,71,76,83],"finite":[38,78],"geometry.":[39],"For":[40,102],"these":[41],"problems,":[44],"we":[45],"show":[46],"dynamics":[50],"associated":[51],"with":[52],"domain":[55,75,87],"are":[56,110,123],"not":[57],"preserved,":[58],"even":[59],"qualitatively,":[60],"by":[61,112],"imposing":[62],"commonly":[64],"used":[65],"form":[66],"artificial":[68],"boundary":[69,84],"condition":[70],"truncate":[72],"domain.":[79],"This":[80],"extreme":[81],"sensitivity":[82],"conditions":[85],"truncation":[88],"direct":[91],"result":[92],"exponential":[95],"ill-conditioning":[96],"underlying":[99],"linearized":[100],"problem.":[101],"Burgers":[103],"equation,":[104],"many":[105],"verified":[111],"calculating":[113],"certain":[114],"explicit":[115],"solutions.":[116],"Some":[117],"related":[118],"ill-conditioned":[119],"problems":[122],"examined.":[124]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}