{"id":"https://openalex.org/W2071288903","doi":"https://doi.org/10.1137/050640047","title":"Stability of Discontinuous Diffusion Coefficients and Initial Conditions in an Inverse Problem for the Heat Equation","display_name":"Stability of Discontinuous Diffusion Coefficients and Initial Conditions in an Inverse Problem for the Heat Equation","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2071288903","doi":"https://doi.org/10.1137/050640047","mag":"2071288903"},"language":"en","primary_location":{"id":"doi:10.1137/050640047","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050640047","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00016490","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035915251","display_name":"Assia Benabdallah","orcid":"https://orcid.org/0000-0001-8583-823X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Assia Benabdallah","raw_affiliation_strings":["Laboratoire d'Analyse, Topologie, Probabilit\u00e9s"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Analyse, Topologie, Probabilit\u00e9s","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086578429","display_name":"Patricia Gaitan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Patricia Gaitan","raw_affiliation_strings":["Laboratoire d'Analyse, Topologie, Probabilit\u00e9s"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Analyse, Topologie, Probabilit\u00e9s","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020320384","display_name":"J\u00e9r\u00f4me Rousseau","orcid":"https://orcid.org/0000-0003-3175-1176"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J\u00e9r\u00f4me Le Rousseau","raw_affiliation_strings":["Laboratoire d'Analyse, Topologie, Probabilit\u00e9s"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Analyse, Topologie, Probabilit\u00e9s","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035915251"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.8174,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.96750748,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"46","issue":"5","first_page":"1849","last_page":"1881"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9976999759674072,"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/uniqueness","display_name":"Uniqueness","score":0.8099887371063232},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.7113083004951477},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.7087308168411255},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6278413534164429},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.620450496673584},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.602205753326416},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5957249999046326},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.5792070031166077},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5210587382316589},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.48984000086784363},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.47810548543930054},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4706149697303772},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.28533637523651123},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17333656549453735},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09060558676719666},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05704772472381592}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8099887371063232},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7113083004951477},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.7087308168411255},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6278413534164429},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.620450496673584},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.602205753326416},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5957249999046326},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.5792070031166077},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5210587382316589},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.48984000086784363},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.47810548543930054},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4706149697303772},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.28533637523651123},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17333656549453735},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09060558676719666},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05704772472381592},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/050640047","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050640047","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00016490v3","is_oa":true,"landing_page_url":"https://hal.science/hal-00016490","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":"SIAM Journal on Control and Optimization, 2007, 46 (5), pp.1849-1881. ⟨10.1137/050640047⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00016490v3","is_oa":true,"landing_page_url":"https://hal.science/hal-00016490","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":"SIAM Journal on Control and Optimization, 2007, 46 (5), pp.1849-1881. ⟨10.1137/050640047⟩","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W630764638","https://openalex.org/W1527296550","https://openalex.org/W1586623601","https://openalex.org/W2019950961","https://openalex.org/W2030571205","https://openalex.org/W2031305506","https://openalex.org/W2055516200","https://openalex.org/W2057187260","https://openalex.org/W2070090021","https://openalex.org/W2073494671","https://openalex.org/W2101743932","https://openalex.org/W2103680881","https://openalex.org/W2111759884","https://openalex.org/W2163597911"],"related_works":["https://openalex.org/W2963662567","https://openalex.org/W4321473471","https://openalex.org/W2111745843","https://openalex.org/W2389517732","https://openalex.org/W2017622585","https://openalex.org/W3099809193","https://openalex.org/W346881876","https://openalex.org/W2084108921","https://openalex.org/W281041820","https://openalex.org/W2140642796"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,18,22,29,36,48],"heat":[3],"equation":[4],"with":[5,65],"a":[6,26,51,66],"discontinuous":[7,61],"diffusion":[8,19,55],"coefficient":[9,20,56],"and":[10,13,21,38],"give":[11],"uniqueness":[12],"stability":[14],"results":[15],"for":[16],"both":[17],"initial":[23],"condition":[24],"from":[25],"measurement":[27],"of":[28,35,50],"solution":[30],"on":[31],"an":[32,63],"arbitrary":[33,41],"part":[34],"boundary":[37],"at":[39],"some":[40],"positive":[42],"time.":[43],"The":[44,54],"key":[45],"ingredient":[46],"is":[47,57],"derivation":[49],"Carleman-type":[52],"estimate.":[53],"assumed":[58],"to":[59],"be":[60],"across":[62],"interface":[64],"monotonicity":[67],"condition.":[68]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}