{"id":"https://openalex.org/W4366180285","doi":"https://doi.org/10.1007/s00211-023-01351-1","title":"Lack of superstable trajectories in linear viscoelasticity: a numerical approach","display_name":"Lack of superstable trajectories in linear viscoelasticity: a numerical approach","publication_year":2023,"publication_date":"2023-04-01","ids":{"openalex":"https://openalex.org/W4366180285","doi":"https://doi.org/10.1007/s00211-023-01351-1"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-023-01351-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01351-1","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s00211-023-01351-1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063675442","display_name":"Paola F. Antonietti","orcid":"https://orcid.org/0000-0002-2138-3878"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Paola F. Antonietti","raw_affiliation_strings":["MOX-Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"MOX-Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005336774","display_name":"Lorenzo Liverani","orcid":"https://orcid.org/0000-0003-2538-8868"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Lorenzo Liverani","raw_affiliation_strings":["Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067626421","display_name":"Vittorino Pata","orcid":"https://orcid.org/0000-0001-7691-419X"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Vittorino Pata","raw_affiliation_strings":["Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milan, Italy","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5063675442"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.547,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64048927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"153","issue":"4","first_page":"611","last_page":"633"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998000264167786,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9984999895095825,"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/algorithm","display_name":"Algorithm","score":0.44345518946647644},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2077661156654358}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44345518946647644},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2077661156654358}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00211-023-01351-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01351-1","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:boa.unimib.it:10281/414698","is_oa":true,"landing_page_url":"https://hdl.handle.net/10281/414698","pdf_url":"https://boa.unimib.it/bitstream/10281/414698/1/Antonietti-2023-Numer%20Math-VoR.pdf","source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:re.public.polimi.it:11311/1235746","is_oa":true,"landing_page_url":"https://link.springer.com/article/10.1007/s00211-023-01351-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-023-01351-1.pdf","source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00211-023-01351-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-023-01351-1","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1162133770","display_name":null,"funder_award_id":"2020F3NCPX","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G8063117722","display_name":null,"funder_award_id":"20204LN5N5","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G895849949","display_name":null,"funder_award_id":"MIUR-PRIN","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G924608660","display_name":null,"funder_award_id":"Math4I4","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320324039","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1527296550","https://openalex.org/W1529316362","https://openalex.org/W1596150805","https://openalex.org/W1606157354","https://openalex.org/W1965600272","https://openalex.org/W1969013469","https://openalex.org/W1973169972","https://openalex.org/W1989914555","https://openalex.org/W1998460280","https://openalex.org/W2000867775","https://openalex.org/W2004848136","https://openalex.org/W2025122482","https://openalex.org/W2028624058","https://openalex.org/W2029230994","https://openalex.org/W2055011057","https://openalex.org/W2060953354","https://openalex.org/W2063946680","https://openalex.org/W2077933954","https://openalex.org/W2081505858","https://openalex.org/W2089425614","https://openalex.org/W2097227533","https://openalex.org/W2267297549","https://openalex.org/W2338052660","https://openalex.org/W2413564584","https://openalex.org/W2497527982","https://openalex.org/W2810364640","https://openalex.org/W2962878408","https://openalex.org/W2963313910","https://openalex.org/W2992124604","https://openalex.org/W3099017241","https://openalex.org/W3149640912","https://openalex.org/W4212817853","https://openalex.org/W4240596267","https://openalex.org/W4245139583","https://openalex.org/W4253874936"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2317200988","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2947381795"],"abstract_inverted_index":{"Abstract":[0],"Given":[1],"a":[2,11],"positive":[3],"operator":[4],"A":[5,32],"on":[6],"some":[7],"Hilbert":[8],"space,":[9],"and":[10,295],"nonnegative":[12],"decreasing":[13],"summable":[14],"function":[15],"$$\\mu":[16,266,289],"$$":[17,267,290],"<mml:math":[18,40,134,268,291],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[19,41,135,269,292],"<mml:mi>\u03bc</mml:mi>":[20,70,160,208,270,293],"</mml:math>":[21,94,244,271,294],",":[22],"we":[23],"consider":[24],"the":[25,96,113,116,260,263,279,286,297],"abstract":[26],"equation":[27,281],"with":[28],"memory":[29,264,287],"$$\\begin{aligned}":[30,118],"\\ddot{u}(t)+":[31],"u(t)-":[33],"\\int":[34],"_0^t":[35],"\\mu":[36],"(s)Au(t-s)":[37],"ds=0":[38],"\\end{aligned}$$":[39,133],"<mml:mrow>":[42,46,51,59,71,78,136,140,142,148,159,161,168,173,183,192,193,209,215,218,225],"<mml:mtable>":[43,137],"<mml:mtr>":[44,138],"<mml:mtd>":[45,139],"<mml:mover>":[47,187],"<mml:mi>u</mml:mi>":[48,58,77,172,188,217,224],"<mml:mo>\u00a8</mml:mo>":[49],"</mml:mover>":[50,190],"<mml:mo>(</mml:mo>":[52,60,72,79,143,149,162,174,194,210,219,226],"<mml:mi>t</mml:mi>":[53,61,68,80,144,156,175,195,206,220,227],"<mml:mo>)</mml:mo>":[54,62,74,83,145,164,169,176,196,212,221,230],"</mml:mrow>":[55,63,75,84,89,93,146,150,165,170,177,179,186,197,199,213,222,231,233,239,243],"<mml:mo>+</mml:mo>":[56,184,202],"<mml:mi>A</mml:mi>":[57,76],"<mml:mo>-</mml:mo>":[64,81,152,223,228],"<mml:msubsup>":[65,153,158,203,214],"<mml:mo>\u222b</mml:mo>":[66,154,204],"<mml:mn>0</mml:mn>":[67,88,155,205],"</mml:msubsup>":[69,157,182,207,236],"<mml:mi>s</mml:mi>":[73,82,86,163,167,211,229,238],"<mml:mi>d</mml:mi>":[85,166,237],"<mml:mo>=</mml:mo>":[87,147],"</mml:mtd>":[90,240],"</mml:mtr>":[91,241],"</mml:mtable>":[92,242],"modeling":[95],"dynamics":[97],"of":[98,104,112,245,262,285,296],"linearly":[99],"viscoelastic":[100],"solids.":[101],"The":[102],"purpose":[103],"this":[105],"work":[106],"is":[107],"to":[108],"provide":[109],"numerical":[110],"evidence":[111],"fact":[114],"that":[115],"energy":[117],"{{\\textsf{E}}}(t)=\\Big":[119],"(1-\\int":[120],"_0^t\\mu":[121,129],"(s)ds\\Big":[122],")\\Vert":[123],"u(t)\\Vert":[124],"^2_1+\\Vert":[125],"\\dot{u}(t)\\Vert":[126],"^2":[127],"+\\int":[128],"(s)\\Vert":[130],"u(t)-u(t-s)\\Vert":[131],"^2_1ds":[132],"<mml:mi>E</mml:mi>":[141],"<mml:mn>1</mml:mn>":[151,180,234],"<mml:mo>\u2016</mml:mo>":[171,178,185,198,216,232],"<mml:mn>2</mml:mn>":[181,200,235],"<mml:mo>\u02d9</mml:mo>":[189],"<mml:msup>":[191],"</mml:msup>":[201],"any":[246],"nontrivial":[247],"solution":[248],"cannot":[249],"decay":[250,261],"faster":[251],"than":[252],"exponential,":[253],"no":[254],"matter":[255],"how":[256],"fast":[257],"might":[258],"be":[259,275],"kernel":[265,288],".":[272],"This":[273],"will":[274],"accomplished":[276],"by":[277],"simulating":[278],"integro-differential":[280],"for":[282],"different":[283],"choices":[284],"initial":[298],"data.":[299]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-02T15:55:50.835912","created_date":"2023-04-19T00:00:00"}