{"id":"https://openalex.org/W4415133832","doi":"https://doi.org/10.48550/arxiv.2506.02595","title":"Numerical methods for fully nonlinear degenerate diffusions","display_name":"Numerical methods for fully nonlinear degenerate diffusions","publication_year":2025,"publication_date":"2025-06-03","ids":{"openalex":"https://openalex.org/W4415133832","doi":"https://doi.org/10.48550/arxiv.2506.02595"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2506.02595","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.02595","pdf_url":"https://arxiv.org/pdf/2506.02595","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2506.02595","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055587166","display_name":"Edgard A. Pimentel","orcid":"https://orcid.org/0000-0002-6420-0410"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pimentel, Edgard A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059802527","display_name":"Erc\u0131\u0301lia Sousa","orcid":"https://orcid.org/0000-0003-4021-4559"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sousa, Erc\u00edlia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9829000234603882,"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":0.9829000234603882,"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":0.9379000067710876,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.7681000232696533},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.741599977016449},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5404999852180481},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5224999785423279},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5070000290870667},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5030999779701233},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4853000044822693},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4251999855041504},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.42309999465942383}],"concepts":[{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.7681000232696533},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.741599977016449},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6858999729156494},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.555400013923645},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5404999852180481},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5224999785423279},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5070000290870667},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5030999779701233},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4853000044822693},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4251999855041504},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.42309999465942383},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.398499995470047},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.3977999985218048},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.38589999079704285},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.31679999828338623},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C154416045","wikidata":"https://www.wikidata.org/wiki/Q5500196","display_name":"Free boundary problem","level":3,"score":0.275299996137619},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C148864181","wikidata":"https://www.wikidata.org/wiki/Q4949969","display_name":"Boundary problem","level":3,"score":0.2524999976158142},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2506.02595","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.02595","pdf_url":"https://arxiv.org/pdf/2506.02595","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"doi:10.48550/arxiv.2506.02595","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.02595","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2506.02595","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.02595","pdf_url":"https://arxiv.org/pdf/2506.02595","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[{"id":"https://openalex.org/G1499778340","display_name":"Center for Mathematics, University of Coimbra","funder_award_id":"UIDB/00324/2020","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G3271324473","display_name":null,"funder_award_id":"DOI 10.54499/UIDB/00324/2020","funder_id":"https://openalex.org/F4320323642","funder_display_name":"Minist\u00e9rio da Ci\u00eancia, Tecnologia e Ensino Superior"},{"id":"https://openalex.org/G4941397794","display_name":null,"funder_award_id":"UIDB/00324/2020","funder_id":"https://openalex.org/F4320323392","funder_display_name":"Universidade de Coimbra"},{"id":"https://openalex.org/G8832587989","display_name":null,"funder_award_id":"10.54499/UIDB/00324/2020","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"}],"funders":[{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"},{"id":"https://openalex.org/F4320323392","display_name":"Universidade de Coimbra","ror":"https://ror.org/04z8k9a98"},{"id":"https://openalex.org/F4320323642","display_name":"Minist\u00e9rio da Ci\u00eancia, Tecnologia e Ensino Superior","ror":"https://ror.org/045b9pr88"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415133832.pdf","grobid_xml":"https://content.openalex.org/works/W4415133832.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,83],"propose":[1],"finite":[2],"difference":[3],"methods":[4,92],"for":[5],"degenerate":[6,64],"fully":[7],"nonlinear":[8],"elliptic":[9,50],"equations":[10],"and":[11,25,95],"prove":[12],"the":[13,16,22,45,49,53,57,61,76,80],"convergence":[14],"of":[15,31,36,63,79,105],"schemes.":[17],"Our":[18,91],"focus":[19],"is":[20,39],"on":[21],"pure":[23],"equation":[24],"a":[26,40,102],"related":[27],"free":[28,58],"boundary":[29,59],"problem":[30],"transmission":[32],"type.":[33],"The":[34],"cornerstone":[35],"our":[37,88,96],"argument":[38],"regularisation":[41],"procedure.":[42],"It":[43],"decouples":[44],"degeneracy":[46],"term":[47],"from":[48],"operator":[51],"driving":[52],"diffusion":[54],"process.":[55],"In":[56],"setting,":[60],"absence":[62],"ellipticity":[65],"entails":[66],"new,":[67],"genuine":[68],"difficulties.":[69],"To":[70],"bypass":[71],"them,":[72],"we":[73],"resort":[74],"to":[75,101],"intrinsic":[77],"properties":[78],"regularised":[81],"problem.":[82],"present":[84],"numerical":[85],"experiments":[86],"supporting":[87],"theoretical":[89],"results.":[90],"are":[93],"flexible,":[94],"approach":[97],"can":[98],"be":[99],"extended":[100],"broader":[103],"class":[104],"non-variational":[106],"problems.":[107]},"counts_by_year":[],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-14T00:00:00"}
