{"id":"https://openalex.org/W1968739458","doi":"https://doi.org/10.1137/050629951","title":"Solutions to a Model with Nonuniformly Parabolic Terms for Phase Evolution Driven by Configurational Forces","display_name":"Solutions to a Model with Nonuniformly Parabolic Terms for Phase Evolution Driven by Configurational Forces","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1968739458","doi":"https://doi.org/10.1137/050629951","mag":"1968739458"},"language":"en","primary_location":{"id":"doi:10.1137/050629951","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050629951","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/A5079892864","display_name":"Hans\u2010Dieter Alber","orcid":"https://orcid.org/0000-0002-0086-8200"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hans-Dieter Alber","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100628275","display_name":"Peicheng Zhu","orcid":"https://orcid.org/0000-0003-3324-9163"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peicheng Zhu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079892864"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.01,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.75974462,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"66","issue":"2","first_page":"680","last_page":"699"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9987000226974487,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9970999956130981,"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/nonlinear-system","display_name":"Nonlinear system","score":0.6647484302520752},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6257658004760742},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6152876615524292},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5988291501998901},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5930050015449524},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5624264478683472},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5543001294136047},{"id":"https://openalex.org/keywords/evolution-equation","display_name":"Evolution equation","score":0.5243690013885498},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4985976219177246},{"id":"https://openalex.org/keywords/elasticity","display_name":"Elasticity (physics)","score":0.4641491174697876},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3502592444419861},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20165657997131348},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10539701581001282},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.08750423789024353},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08335486054420471}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6647484302520752},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6257658004760742},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6152876615524292},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5988291501998901},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5930050015449524},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5624264478683472},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5543001294136047},{"id":"https://openalex.org/C2982905333","wikidata":"https://www.wikidata.org/wiki/Q1156744","display_name":"Evolution equation","level":2,"score":0.5243690013885498},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4985976219177246},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.4641491174697876},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3502592444419861},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20165657997131348},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10539701581001282},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.08750423789024353},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08335486054420471},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050629951","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050629951","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"},{"id":"pmh:oai:tubiblio.ulb.tu-darmstadt.de:27650","is_oa":false,"landing_page_url":"http://tubiblio.ulb.tu-darmstadt.de/27650/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196390","display_name":"TUbilio (Technical University of Darmstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31512782","host_organization_name":"Technische Universit\u00e4t Darmstadt","host_organization_lineage":["https://openalex.org/I31512782"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.49000000953674316}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1967463968","https://openalex.org/W1992162278","https://openalex.org/W2001345036","https://openalex.org/W2054146295","https://openalex.org/W2062676931","https://openalex.org/W2082984522","https://openalex.org/W2095303583","https://openalex.org/W2096597131","https://openalex.org/W2160771099","https://openalex.org/W2369386221","https://openalex.org/W2728242908","https://openalex.org/W2754089436","https://openalex.org/W3091814460","https://openalex.org/W4244617393","https://openalex.org/W4253555402"],"related_works":["https://openalex.org/W1967450583","https://openalex.org/W2066764747","https://openalex.org/W2385175414","https://openalex.org/W2083817219","https://openalex.org/W2264582182","https://openalex.org/W4389325770","https://openalex.org/W3047860677","https://openalex.org/W2969693569","https://openalex.org/W2343093002","https://openalex.org/W1850237974"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,24,41,89,92],"existence":[3,84],"of":[4,17,23,26,35,45,80,91],"solutions":[5],"global":[6],"in":[7,43,97],"time":[8,44],"to":[9,76,88],"an":[10],"initial-boundary":[11],"value":[12],"problem":[13,39],"for":[14],"a":[15,30,60,78],"system":[16],"partial":[18],"differential":[19],"equations,":[20],"which":[21,86],"consists":[22],"equations":[25],"linear":[27],"elasticity":[28],"and":[29,72],"nonlinear":[31],"nonuniformly":[32],"parabolic":[33],"equation":[34],"second":[36],"order.":[37],"The":[38],"models":[40],"behavior":[42],"materials":[46],"with":[47,53,62],"martensitic":[48],"phase":[49,55],"transformations.":[50],"This":[51],"model":[52,61],"diffusive":[54],"interfaces":[56],"was":[57],"derived":[58],"from":[59],"sharp":[63],"interfaces,":[64],"whose":[65],"evolution":[66],"is":[67,94],"driven":[68],"by":[69],"configurational":[70],"forces,":[71],"can":[73],"be":[74,77],"considered":[75],"regularization":[79],"that":[81],"model.":[82],"Our":[83],"proof,":[85],"contributes":[87],"verification":[90],"model,":[93],"only":[95],"valid":[96],"one":[98],"space":[99],"dimension.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
