{"id":"https://openalex.org/W2043184112","doi":"https://doi.org/10.1137/130915959","title":"Interface Dynamics in Discrete Forward-Backward Diffusion Equations","display_name":"Interface Dynamics in Discrete Forward-Backward Diffusion Equations","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2043184112","doi":"https://doi.org/10.1137/130915959","mag":"2043184112"},"language":"en","primary_location":{"id":"doi:10.1137/130915959","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130915959","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1304.1693","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032118756","display_name":"Michael Helmers","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]},{"id":"https://openalex.org/I4210123467","display_name":"Institut f\u00fcr Angewandte Statistik","ror":"https://ror.org/03abd2075","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210123467"]},{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael Helmers","raw_affiliation_strings":[", Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn","Fachrichtung Mathematik, Universit\u00e4t des Saarlandes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":", Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn","institution_ids":["https://openalex.org/I135140700","https://openalex.org/I4210123467"]},{"raw_affiliation_string":"Fachrichtung Mathematik, Universit\u00e4t des Saarlandes","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101403112","display_name":"Michael Herrmann","orcid":"https://orcid.org/0000-0002-5488-9824"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]},{"id":"https://openalex.org/I4210123467","display_name":"Institut f\u00fcr Angewandte Statistik","ror":"https://ror.org/03abd2075","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210123467"]},{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael Herrmann","raw_affiliation_strings":[", Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn","Fachrichtung Mathematik, Universit\u00e4t des Saarlandes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":", Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn","institution_ids":["https://openalex.org/I135140700","https://openalex.org/I4210123467"]},{"raw_affiliation_string":"Fachrichtung Mathematik, Universit\u00e4t des Saarlandes","institution_ids":["https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3562,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.649135,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"4","first_page":"1261","last_page":"1297"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"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"}},"topics":[{"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"}},{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9979000091552734,"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"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9754999876022339,"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":0.6045135855674744},{"id":"https://openalex.org/keywords/bistability","display_name":"Bistability","score":0.5697188973426819},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5579485893249512},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4705002009868622},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4654358923435211},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46460193395614624},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.433779776096344},{"id":"https://openalex.org/keywords/scaling-limit","display_name":"Scaling limit","score":0.43037787079811096},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4211256206035614},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4023084044456482},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3091389834880829},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12559887766838074}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6045135855674744},{"id":"https://openalex.org/C97292510","wikidata":"https://www.wikidata.org/wiki/Q2304620","display_name":"Bistability","level":2,"score":0.5697188973426819},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5579485893249512},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4705002009868622},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4654358923435211},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46460193395614624},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.433779776096344},{"id":"https://openalex.org/C24084028","wikidata":"https://www.wikidata.org/wiki/Q7429781","display_name":"Scaling limit","level":3,"score":0.43037787079811096},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4211256206035614},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4023084044456482},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3091389834880829},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12559887766838074},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/130915959","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130915959","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1304.1693","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.1693","pdf_url":"https://arxiv.org/pdf/1304.1693","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:CiteSeerX.psu:10.1.1.299.9598","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.299.9598","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uni-sb.de/service/preprints/preprint331.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.769.6231","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.769.6231","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1304.1693.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1304.1693","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.1693","pdf_url":"https://arxiv.org/pdf/1304.1693","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1526521272","https://openalex.org/W1965052842","https://openalex.org/W1976185024","https://openalex.org/W1988786426","https://openalex.org/W2016257486","https://openalex.org/W2027372885","https://openalex.org/W2042401506","https://openalex.org/W2044981349","https://openalex.org/W2046906471","https://openalex.org/W2049794413","https://openalex.org/W2054803818","https://openalex.org/W2080395269","https://openalex.org/W2123236393","https://openalex.org/W2150134853","https://openalex.org/W2245508946","https://openalex.org/W2331519894","https://openalex.org/W3038086992"],"related_works":["https://openalex.org/W4224217224","https://openalex.org/W1964519618","https://openalex.org/W3118640947","https://openalex.org/W4388308731","https://openalex.org/W1969697984","https://openalex.org/W3048730783","https://openalex.org/W1992416820","https://openalex.org/W3094197880","https://openalex.org/W2183786486","https://openalex.org/W2029082315"],"abstract_inverted_index":{"We":[0,53,113],"study":[1],"the":[2,25,29,37,55,86,95,101,123,130,138,154,157,161,174],"motion":[3],"of":[4,36,57,69,88,116,156,176],"phase":[5],"interfaces":[6],"in":[7,28,173],"a":[8,17,74,80,108,149],"diffusive":[9],"lattice":[10,159],"equation":[11],"with":[12,21,40,79],"bistable":[13,42],"nonlinearity":[14],"and":[15,44,50,60,67,91,107,127,165],"derive":[16,119,169],"free":[18,139],"boundary":[19,140],"problem":[20],"hysteresis":[22],"to":[23,47,145,160,168],"describe":[24],"macroscopic":[26,58,124,131,170],"evolution":[27],"parabolic":[30],"scaling":[31],"limit.":[32],"The":[33,142],"first":[34],"part":[35],"paper":[38],"deals":[39],"general":[41],"nonlinearities":[43],"is":[45,148],"restricted":[46],"numerical":[48,62],"experiments":[49],"heuristic":[51],"arguments.":[52],"discuss":[54],"formation":[56],"data":[59,106],"present":[61],"evidence":[63],"for":[64,104,122],"pinning,":[65],"depinning,":[66],"annihilation":[68],"interfaces.":[70,93],"Afterwards":[71],"we":[72,98],"identify":[73],"generalized":[75],"Stefan":[76],"condition":[77],"along":[78],"hysteretic":[81],"flow":[82],"rule":[83],"that":[84,129,152],"characterize":[85],"dynamics":[87,103],"both":[89],"standing":[90],"moving":[92],"In":[94],"second":[96],"part,":[97],"rigorously":[99],"justify":[100],"limit":[102,132],"single-interface":[105],"special":[109],"piecewise":[110],"affine":[111],"nonlinearity.":[112],"prove":[114],"persistence":[115],"such":[117],"data,":[118],"upper":[120],"bounds":[121],"interface":[125],"speed,":[126],"show":[128],"can":[133],"indeed":[134],"be":[135],"described":[136],"by":[137],"problem.":[141],"fundamental":[143],"ingredient":[144],"our":[146],"proofs":[147],"representation":[150],"formula":[151],"links":[153],"solutions":[155],"nonlinear":[158],"discrete":[162],"heat":[163],"kernel":[164],"enables":[166],"us":[167],"compactness":[171],"results":[172],"space":[175],"continuous":[177],"functions.":[178]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
