{"id":"https://openalex.org/W3090531495","doi":"https://doi.org/10.3934/nhm.2021007","title":"Coupling techniques for nonlinear hyperbolic equations. \u2161. resonant interfaces with internal structure","display_name":"Coupling techniques for nonlinear hyperbolic equations. \u2161. resonant interfaces with internal structure","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3090531495","doi":"https://doi.org/10.3934/nhm.2021007","mag":"3090531495"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2021007","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021007","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=09a3766d-45d9-4f9c-997b-daa764369b35","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks &amp; Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=09a3766d-45d9-4f9c-997b-daa764369b35","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068225761","display_name":"Benjamin Boutin","orcid":"https://orcid.org/0000-0002-4012-6922"},"institutions":[{"id":"https://openalex.org/I4210161663","display_name":"Institut de recherche math\u00e9matique de Rennes","ror":"https://ror.org/05y76vp22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2800285241","https://openalex.org/I28221208","https://openalex.org/I3124938446","https://openalex.org/I4210117091","https://openalex.org/I4210141950","https://openalex.org/I4210146044","https://openalex.org/I4210161663","https://openalex.org/I4399657933","https://openalex.org/I56067802","https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Benjamin Boutin","raw_affiliation_strings":["IRMAR - Institut de Recherche Math\u00e9matique de Rennes (Campus de Beaulieu, b\u00e2timents 22 et 23, \r\n263 avenue du G\u00e9n\u00e9ral Leclerc, CS 74205\r\n35042  RENNES C\u00e9dex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRMAR - Institut de Recherche Math\u00e9matique de Rennes (Campus de Beaulieu, b\u00e2timents 22 et 23, \r\n263 avenue du G\u00e9n\u00e9ral Leclerc, CS 74205\r\n35042  RENNES C\u00e9dex - France)","institution_ids":["https://openalex.org/I4210161663"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113797855","display_name":"Fr\u00e9\u0301d\u00e9\u0301ric Coquel","orcid":null},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210107641","display_name":"Centre de Math\u00e9matiques Appliqu\u00e9es de l'\u00c9cole polytechnique","ror":"https://ror.org/012e1xn46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210107641","https://openalex.org/I4210141950","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Coquel","raw_affiliation_strings":["CMAP - Centre de Math\u00e9matiques Appliqu\u00e9es de l'Ecole polytechnique (Route de Saclay, 91128 Palaiseau Cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CMAP - Centre de Math\u00e9matiques Appliqu\u00e9es de l'Ecole polytechnique (Route de Saclay, 91128 Palaiseau Cedex - France)","institution_ids":["https://openalex.org/I4210107641","https://openalex.org/I142476485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035830456","display_name":"Philippe G. LeFloch","orcid":"https://orcid.org/0000-0002-9546-0784"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Philippe G. LeFloch","raw_affiliation_strings":["LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions (Sorbonne-Universit\u00e9, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions (Sorbonne-Universit\u00e9, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5068225761"],"corresponding_institution_ids":["https://openalex.org/I4210161663"],"apc_list":null,"apc_paid":null,"fwci":0.9904,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6935167,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"16","issue":"2","first_page":"283","last_page":"283"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9995999932289124,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9995999932289124,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9994000196456909,"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":0.9983000159263611,"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/nonlinear-system","display_name":"Nonlinear system","score":0.7141143083572388},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5642021298408508},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5098029971122742},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.500190019607544},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.48331236839294434},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4416868984699249},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.43167799711227417},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34194231033325195},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3313409090042114},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19122233986854553},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14923179149627686},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.10358890891075134}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7141143083572388},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5642021298408508},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5098029971122742},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.500190019607544},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.48331236839294434},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4416868984699249},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.43167799711227417},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34194231033325195},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3313409090042114},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19122233986854553},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14923179149627686},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.10358890891075134},{"id":"https://openalex.org/C191897082","wikidata":"https://www.wikidata.org/wiki/Q11467","display_name":"Metallurgy","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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":4,"locations":[{"id":"doi:10.3934/nhm.2021007","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021007","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=09a3766d-45d9-4f9c-997b-daa764369b35","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks &amp; Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2010.01565","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.01565","pdf_url":"https://arxiv.org/pdf/2010.01565","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-02962629v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02962629","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, 2021, 16 (2), pp.283-315. &#x27E8;10.3934/nhm.2021007&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:dba910672fa540408f5e2fa950cea46a","is_oa":false,"landing_page_url":"https://doaj.org/article/dba910672fa540408f5e2fa950cea46a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 16, Iss 2, Pp 283-315 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2021007","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021007","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=09a3766d-45d9-4f9c-997b-daa764369b35","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks &amp; Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3090531495.pdf","grobid_xml":"https://content.openalex.org/works/W3090531495.grobid-xml"},"referenced_works_count":66,"referenced_works":["https://openalex.org/W86125560","https://openalex.org/W115528814","https://openalex.org/W1544533473","https://openalex.org/W1544776024","https://openalex.org/W1590353515","https://openalex.org/W1963921981","https://openalex.org/W1971338560","https://openalex.org/W1975048198","https://openalex.org/W1975772261","https://openalex.org/W1976197236","https://openalex.org/W1985631557","https://openalex.org/W1987240746","https://openalex.org/W1988206114","https://openalex.org/W1989037733","https://openalex.org/W1989276049","https://openalex.org/W1992812527","https://openalex.org/W1993392273","https://openalex.org/W1994609182","https://openalex.org/W1999292150","https://openalex.org/W1999461763","https://openalex.org/W2000980802","https://openalex.org/W2003706795","https://openalex.org/W2004934375","https://openalex.org/W2007031446","https://openalex.org/W2018342837","https://openalex.org/W2019473179","https://openalex.org/W2024097616","https://openalex.org/W2029811565","https://openalex.org/W2038831503","https://openalex.org/W2039594536","https://openalex.org/W2056889585","https://openalex.org/W2059991999","https://openalex.org/W2060527622","https://openalex.org/W2061726168","https://openalex.org/W2066625432","https://openalex.org/W2069973298","https://openalex.org/W2070543376","https://openalex.org/W2075610411","https://openalex.org/W2077620382","https://openalex.org/W2090076044","https://openalex.org/W2092435235","https://openalex.org/W2144537212","https://openalex.org/W2254772253","https://openalex.org/W2261284007","https://openalex.org/W2284764808","https://openalex.org/W2325204788","https://openalex.org/W2330783814","https://openalex.org/W2338332680","https://openalex.org/W2481459718","https://openalex.org/W2592500796","https://openalex.org/W2963882701","https://openalex.org/W2963943378","https://openalex.org/W2964126157","https://openalex.org/W2964305951","https://openalex.org/W2964330159","https://openalex.org/W2983543841","https://openalex.org/W3002325980","https://openalex.org/W3101554515","https://openalex.org/W3102306170","https://openalex.org/W4232258220","https://openalex.org/W4238313514","https://openalex.org/W4250741917","https://openalex.org/W4289022055","https://openalex.org/W4298426431","https://openalex.org/W4300774331","https://openalex.org/W4388322678"],"related_works":["https://openalex.org/W2154204858","https://openalex.org/W3209622820","https://openalex.org/W4254199101","https://openalex.org/W4300427796","https://openalex.org/W2382250648","https://openalex.org/W1670153145","https://openalex.org/W2367363545","https://openalex.org/W2586383879","https://openalex.org/W2067895158","https://openalex.org/W2071749707"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>In":[1],"the":[2,26,36,42,52,61,65,76,85,105],"first":[3],"part":[4],"of":[5,38,55,64],"this":[6,49],"series,":[7],"an":[8],"augmented":[9],"PDE":[10],"system":[11],"was":[12],"introduced":[13],"in":[14,51,67,81],"order":[15,68],"to":[16,34,41,69,83],"couple":[17],"two":[18],"nonlinear":[19],"hyperbolic":[20],"equations":[21,58],"together.":[22],"This":[23],"formulation":[24],"allowed":[25],"authors,":[27],"based":[28],"on":[29],"Dafermos's":[30],"self-similar":[31,39],"viscosity":[32],"method,":[33],"establish":[35],"existence":[37],"solutions":[40,99,115],"coupled":[43],"Riemann":[44],"problem.":[45],"We":[46,107],"continue":[47],"here":[48],"analysis":[50],"restricted":[53],"case":[54],"one-dimensional":[56],"scalar":[57],"and":[59],"investigate":[60],"internal":[62],"structure":[63],"interface":[66,87],"derive":[70],"a":[71,93],"selection":[72],"criterion":[73,95],"associated":[74],"with":[75,121],"underlying":[77],"regularization":[78],"mechanism":[79],"and,":[80],"turn,":[82],"characterize":[84],"nonconservative":[86],"layer.":[88],"In":[89],"addition,":[90],"we":[91],"identify":[92],"new":[94],"that":[96,100,113],"selects":[97],"double-waved":[98],"are":[101],"also":[102],"continuous":[103],"at":[104],"interface.":[106],"conclude":[108],"by":[109],"providing":[110],"some":[111],"evidence":[112],"such":[114],"can":[116],"be":[117],"non-unique":[118],"when":[119],"dealing":[120],"non-convex":[122],"flux-functions.":[123]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}