{"id":"https://openalex.org/W2044565541","doi":"https://doi.org/10.1090/s0025-5718-99-01063-7","title":"Numerical solution of a fast diffusion equation","display_name":"Numerical solution of a fast diffusion equation","publication_year":1999,"publication_date":"1999-04-01","ids":{"openalex":"https://openalex.org/W2044565541","doi":"https://doi.org/10.1090/s0025-5718-99-01063-7","mag":"2044565541"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-99-01063-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01063-7","pdf_url":"https://www.ams.org/mcom/1999-68-226/S0025-5718-99-01063-7/S0025-5718-99-01063-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1999-68-226/S0025-5718-99-01063-7/S0025-5718-99-01063-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011631328","display_name":"Marie-No\u00eblle Le Roux","orcid":null},"institutions":[{"id":"https://openalex.org/I4210094417","display_name":"CEA Gramat","ror":"https://ror.org/00j8epd55","country_code":"FR","type":"government","lineage":["https://openalex.org/I4210094417","https://openalex.org/I4210101455"]},{"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":true,"raw_author_name":"Marie-Noelle Le Roux","raw_affiliation_strings":["GRAMM-Math\u00c3\u00a9matiques, 351, cours de la Lib\u00c3\u00a9ration, F-33405 Talence Cedex, France","GRAMM-Math\u00e9matiques, 351, cours de la Lib\u00e9ration, F-33405 Talence Cedex, France"],"affiliations":[{"raw_affiliation_string":"GRAMM-Math\u00c3\u00a9matiques, 351, cours de la Lib\u00c3\u00a9ration, F-33405 Talence Cedex, France","institution_ids":["https://openalex.org/I4210094417"]},{"raw_affiliation_string":"GRAMM-Math\u00e9matiques, 351, cours de la Lib\u00e9ration, F-33405 Talence Cedex, France","institution_ids":["https://openalex.org/I4210166017"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091006322","display_name":"Paul-\u00c9mile Maing\u00e9","orcid":"https://orcid.org/0000-0001-8146-1375"},"institutions":[{"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"]},{"id":"https://openalex.org/I4210094417","display_name":"CEA Gramat","ror":"https://ror.org/00j8epd55","country_code":"FR","type":"government","lineage":["https://openalex.org/I4210094417","https://openalex.org/I4210101455"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Paul-Emile Mainge","raw_affiliation_strings":["GRAMM-Math\u00c3\u00a9matiques, 351, cours de la Lib\u00c3\u00a9ration, F-33405 Talence Cedex, France","GRAMM-Math\u00e9matiques, 351, cours de la Lib\u00e9ration, F-33405 Talence Cedex, France"],"affiliations":[{"raw_affiliation_string":"GRAMM-Math\u00c3\u00a9matiques, 351, cours de la Lib\u00c3\u00a9ration, F-33405 Talence Cedex, France","institution_ids":["https://openalex.org/I4210094417"]},{"raw_affiliation_string":"GRAMM-Math\u00e9matiques, 351, cours de la Lib\u00e9ration, F-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/A5011631328"],"corresponding_institution_ids":["https://openalex.org/I4210094417","https://openalex.org/I4210166017"],"apc_list":null,"apc_paid":null,"fwci":0.4708,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.64702746,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"68","issue":"226","first_page":"461","last_page":"486"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9994999766349792,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9975000023841858,"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/mathematics","display_name":"Mathematics","score":0.8891013860702515},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6795401573181152},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6532608270645142},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6153427362442017},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.560189425945282},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5565066933631897},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.5319358110427856},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5278475284576416},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.5051396489143372},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4737972617149353},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4407043159008026},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.420405775308609},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0716424286365509}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8891013860702515},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6795401573181152},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6532608270645142},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6153427362442017},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.560189425945282},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5565066933631897},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.5319358110427856},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5278475284576416},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.5051396489143372},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4737972617149353},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4407043159008026},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.420405775308609},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0716424286365509},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-99-01063-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01063-7","pdf_url":"https://www.ams.org/mcom/1999-68-226/S0025-5718-99-01063-7/S0025-5718-99-01063-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-99-01063-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01063-7","pdf_url":"https://www.ams.org/mcom/1999-68-226/S0025-5718-99-01063-7/S0025-5718-99-01063-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.41999998688697815,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2044565541.pdf","grobid_xml":"https://content.openalex.org/works/W2044565541.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W114786621","https://openalex.org/W116809156","https://openalex.org/W1976938383","https://openalex.org/W1978551359","https://openalex.org/W1983760800","https://openalex.org/W1998233671","https://openalex.org/W2012166560","https://openalex.org/W2036706294","https://openalex.org/W2045492523","https://openalex.org/W2048863565","https://openalex.org/W2064698982","https://openalex.org/W2071415470","https://openalex.org/W2073078790","https://openalex.org/W2101288394","https://openalex.org/W2318392277","https://openalex.org/W4256310819"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W1971388572","https://openalex.org/W2337838060"],"abstract_inverted_index":{"In":[0],"this":[1,82],"paper,":[2],"the":[3,6,12,32,57,63,77,90,94,115],"authors":[4],"consider":[5],"first":[7],"boundary":[8,35],"value":[9],"problem":[10,83],"for":[11,62,76,106],"nonlinear":[13],"reaction":[14],"diffusion":[15,46],"equation:":[16],"$u_{t}-\\Delta":[17],"u^{m}=\\alpha":[18],"u^{p_{1}}$":[19],"in":[20,26,70,79],"$\\Omega$,":[21],"a":[22,39,71,103],"smooth":[23],"bounded":[24],"domain":[25],"$\\mathbb":[27],"{R}^{d}":[28],"(d\\geq":[29],"1)$":[30],"with":[31,38],"zero":[33],"lateral":[34],"condition":[36],"and":[37,51],"positive":[40],"initial":[41,58,95],"condition,":[42],"$m\\in":[43],"]0,1[$":[44],"(fast":[45],"problem),":[47],"$\\alpha":[48],"\\geq":[49],"0$":[50],"$p_{1}\\geq":[52],"m$.":[53],"Sufficient":[54],"conditions":[55],"on":[56],"data":[59],"are":[60],"obtained":[61],"solution":[64],"to":[65],"vanish":[66],"or":[67,102],"become":[68],"infinite":[69],"finite":[72],"time.":[73],"A":[74],"scheme":[75,88],"discretization":[78],"time":[80],"of":[81,93,99,114],"is":[84,117],"proposed.":[85],"The":[86,112],"numerical":[87],"preserves":[89],"essential":[91],"properties":[92],"problem;":[96],"namely":[97],"existence":[98],"an":[100],"extinction":[101],"blow-up":[104],"time,":[105],"which":[107],"estimates":[108],"have":[109],"been":[110],"obtained.":[111],"convergence":[113],"method":[116],"also":[118],"proved.":[119]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
