{"id":"https://openalex.org/W2899521243","doi":"https://doi.org/10.3934/nhm.2018028","title":"Effective interface conditions for processes through thin heterogeneous layers with nonlinear transmission at the microscopic bulk-layer interface","display_name":"Effective interface conditions for processes through thin heterogeneous layers with nonlinear transmission at the microscopic bulk-layer interface","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2899521243","doi":"https://doi.org/10.3934/nhm.2018028","mag":"2899521243"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2018028","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2018028","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks &amp; Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/nhm.2018028","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072887891","display_name":"Markus Gahn","orcid":"https://orcid.org/0000-0002-2216-145X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Markus Gahn","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016648054","display_name":"Maria Neuss\u2010Radu","orcid":"https://orcid.org/0000-0003-1788-5354"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maria Neuss-Radu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073728063","display_name":"Peter Knabner","orcid":"https://orcid.org/0000-0003-2141-4889"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peter Knabner","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072887891"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3642,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.9033675,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"13","issue":"4","first_page":"609","last_page":"640"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998000264167786,"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":0.9998000264167786,"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":0.98580002784729,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.982699990272522,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6426061391830444},{"id":"https://openalex.org/keywords/interface","display_name":"Interface (matter)","score":0.6423696279525757},{"id":"https://openalex.org/keywords/layer","display_name":"Layer (electronics)","score":0.6044196486473083},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.5302624106407166},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.5064665079116821},{"id":"https://openalex.org/keywords/thin-film","display_name":"Thin film","score":0.4983830451965332},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.484764039516449},{"id":"https://openalex.org/keywords/thermal-diffusivity","display_name":"Thermal diffusivity","score":0.4813866913318634},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4725132882595062},{"id":"https://openalex.org/keywords/thin-layer","display_name":"Thin layer","score":0.4170936346054077},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.401661217212677},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25038206577301025},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2413739562034607},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22661328315734863},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.16476622223854065},{"id":"https://openalex.org/keywords/nanotechnology","display_name":"Nanotechnology","score":0.154992014169693},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.13265210390090942}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6426061391830444},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.6423696279525757},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.6044196486473083},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.5302624106407166},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.5064665079116821},{"id":"https://openalex.org/C19067145","wikidata":"https://www.wikidata.org/wiki/Q1137203","display_name":"Thin film","level":2,"score":0.4983830451965332},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.484764039516449},{"id":"https://openalex.org/C37668627","wikidata":"https://www.wikidata.org/wiki/Q3381809","display_name":"Thermal diffusivity","level":2,"score":0.4813866913318634},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4725132882595062},{"id":"https://openalex.org/C3019891514","wikidata":"https://www.wikidata.org/wiki/Q7784286","display_name":"Thin layer","level":3,"score":0.4170936346054077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.401661217212677},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25038206577301025},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2413739562034607},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22661328315734863},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.16476622223854065},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.154992014169693},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.13265210390090942},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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},{"id":"https://openalex.org/C196806460","wikidata":"https://www.wikidata.org/wiki/Q188603","display_name":"Capillary action","level":2,"score":0.0},{"id":"https://openalex.org/C28413391","wikidata":"https://www.wikidata.org/wiki/Q785542","display_name":"Capillary number","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2018028","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2018028","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks &amp; Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:eee95928de694f528d02994ff1340856","is_oa":false,"landing_page_url":"https://doaj.org/article/eee95928de694f528d02994ff1340856","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 13, Iss 4, Pp 609-640 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2018028","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2018028","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2385382668","https://openalex.org/W2283102826","https://openalex.org/W2023596821","https://openalex.org/W2351460627","https://openalex.org/W2100701926","https://openalex.org/W1974236007","https://openalex.org/W1969098006","https://openalex.org/W2335514579","https://openalex.org/W2079698632","https://openalex.org/W246352078"],"abstract_inverted_index":{"In":[0],"this":[1,129],"paper,":[2],"we":[3,59,92,131],"consider":[4],"a":[5,11,20,29,61,143],"system":[6],"of":[7,14,25,72,135],"reaction-diffusion":[8],"equations":[9,34],"in":[10,113,156],"domain":[12],"consisting":[13],"two":[15,89],"bulk":[16,90],"regions":[17],"separated":[18],"by":[19],"thin":[21,81,139,158],"layer":[22,37,46,82],"with":[23,97],"thickness":[24],"order":[26],"$\u03b5$":[27,40],"and":[28,41,142],"periodic":[30],"heterogeneous":[31,140],"structure.":[32],"The":[33,104],"inside":[35,44],"the":[36,42,45,56,67,73,80,101,111,114,119,122,125,133,153,157],"depend":[38],"on":[39,47,66,69,121],"diffusivity":[43],"an":[48,85],"additional":[49],"parameter":[50],"$\u03b3":[51],"\u2208":[52],"[-1,":[53],"1]$.":[54],"On":[55],"bulk-layer":[57],"interface,":[58],"assume":[60],"nonlinear":[62,115],"Neumann-transmission":[63],"condition":[64],"depending":[65],"solutions":[68],"both":[70],"sides":[71],"interface.":[74],"For":[75,128],"$\\epsilon":[76],"\\to0":[77],"$,":[78],"when":[79],"reduces":[83],"to":[84,108,110,152],"interface":[86,102,123],"$\u03a3$":[87],"between":[88,124],"domains,":[91],"rigorously":[93],"derive":[94],"macroscopic":[95],"models":[96],"effective":[98],"conditions":[99],"across":[100],"$\u03a3$.":[103],"crucial":[105],"part":[106],"is":[107],"pass":[109],"limit":[112],"terms,":[116],"especially":[117],"for":[118,138,147],"traces":[120],"different":[126],"compartments.":[127],"purpose,":[130],"use":[132],"method":[134],"two-scale":[136],"convergence":[137],"layers,":[141],"Kolmogorov-type":[144],"compactness":[145],"result":[146],"Banach":[148],"valued":[149],"functions,":[150],"applied":[151],"unfolded":[154],"sequence":[155],"layer.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
