{"id":"https://openalex.org/W1966485506","doi":"https://doi.org/10.1137/08073665x","title":"Convergence of Numerical Schemes to a Nonlinear Kinetic Model of Population Dynamics with Nonlocal Boundary Conditions","display_name":"Convergence of Numerical Schemes to a Nonlinear Kinetic Model of Population Dynamics with Nonlocal Boundary Conditions","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1966485506","doi":"https://doi.org/10.1137/08073665x","mag":"1966485506"},"language":"en","primary_location":{"id":"doi:10.1137/08073665x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/08073665x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5066264257","display_name":"Bouchra Aylaj","orcid":"https://orcid.org/0000-0002-4736-806X"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"B. Aylaj","raw_affiliation_strings":["ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics (Inria Bordeaux - France)"],"affiliations":[{"raw_affiliation_string":"ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics (Inria Bordeaux - France)","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110107528","display_name":"A. Noussair","orcid":null},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"A. Noussair","raw_affiliation_strings":["ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics (Inria Bordeaux - France)","IMB - Institut de Math\u00e9matiques de Bordeaux (351 cours de la Lib\u00e9ration 33405 TALENCE CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics (Inria Bordeaux - France)","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"IMB - Institut de Math\u00e9matiques de Bordeaux (351 cours de la Lib\u00e9ration 33405 TALENCE CEDEX - France)","institution_ids":["https://openalex.org/I4210166017"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066264257"],"corresponding_institution_ids":["https://openalex.org/I1326498283"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.06403817,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"48","issue":"5","first_page":"1707","last_page":"1732"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9954000115394592,"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":0.9950000047683716,"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/mathematics","display_name":"Mathematics","score":0.8734106421470642},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6172657012939453},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5473099946975708},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5003101825714111},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4988276958465576},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.4742278754711151},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4653525948524475},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.42255932092666626},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4160149395465851},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4073159098625183}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8734106421470642},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6172657012939453},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5473099946975708},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5003101825714111},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4988276958465576},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.4742278754711151},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4653525948524475},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.42255932092666626},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4160149395465851},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4073159098625183},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/08073665x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/08073665x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00497043v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00497043","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Numerical Analysis, 2010, 48 (5), pp.1707-1732. &#x27E8;10.1137/08073665X&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/115817","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/115817","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","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":"","raw_type":"Article de revue"},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/190126","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/190126","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","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":"","raw_type":"Article de revue"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W196325668","https://openalex.org/W1549748890","https://openalex.org/W1564951438","https://openalex.org/W1596619759","https://openalex.org/W1997155153","https://openalex.org/W2034269086","https://openalex.org/W2042623681","https://openalex.org/W2046052598","https://openalex.org/W2066501150","https://openalex.org/W2077590697","https://openalex.org/W2083321256","https://openalex.org/W2092549217","https://openalex.org/W2104010300","https://openalex.org/W2130541529","https://openalex.org/W2159471657","https://openalex.org/W2912182292","https://openalex.org/W2994868089"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4243074410","https://openalex.org/W4289551052","https://openalex.org/W4390756076","https://openalex.org/W2340777379"],"abstract_inverted_index":{"We":[0,51],"examine":[1],"existence":[2],"and":[3,9,45,68,88,107],"uniqueness":[4],"of":[5,18,25,33,59,94,104],"a":[6,19,23,26,38,42,47,53,57,60,83,101],"global":[7],"solution":[8],"some":[10],"basic":[11],"mathematical":[12],"issues":[13],"associated":[14,63],"with":[15,37,46,64,100],"the":[16,65,73,95,105],"development":[17],"numerical":[20,54],"scheme":[21,55],"for":[22],"model":[24],"tumor-immune":[27],"system":[28,31],"interaction.":[29],"The":[30,76],"consists":[32],"nonlinear":[34],"transport":[35],"equations":[36],"bilinear":[39],"operator":[40,71],"like":[41],"Boltzmann":[43],"type":[44],"nonlocal":[48],"boundary":[49],"condition.":[50],"construct":[52],"as":[56],"combination":[58],"$S(t)$-operator":[61],"semigroup":[62],"continuous":[66],"problem":[67],"$P^\\Delta$":[69],"projection":[70],"on":[72],"discrete":[74],"space.":[75],"three":[77],"estimates,":[78],"(1)":[79],"$L^\\infty$":[80],"bound,":[81,87],"(2)":[82],"uniform":[84],"total":[85],"variation":[86],"(3)":[89],"$L^1$":[90],"continuity":[91],"in":[92],"time":[93],"approximate":[96],"solution,":[97],"are":[98,112],"established":[99],"self-contained":[102],"treatment":[103],"stability":[106],"convergence":[108],"properties.":[109],"Numerical":[110],"calculations":[111],"reported.":[113]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
