{"id":"https://openalex.org/W7220919403","doi":"https://doi.org/10.48550/arxiv.2610.08014","title":"A method of moving planes for a mixed local-nonlocal parabolic system with quenching","display_name":"A method of moving planes for a mixed local-nonlocal parabolic system with quenching","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220919403","doi":"https://doi.org/10.48550/arxiv.2610.08014"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.08014","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08014","pdf_url":"https://arxiv.org/pdf/2610.08014","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.08014","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120591937","display_name":"Sergio Junquera","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I121748325","display_name":"Universidad Complutense de Madrid","ror":"https://ror.org/02p0gd045","country_code":"ES","type":"education","lineage":["https://openalex.org/I121748325"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Junquera, Sergio","raw_affiliation_strings":["Departamento de An\u00e1lisis Matem\u00e1tico y Matem\u00e1tica Aplicada , Universidad Complutense de Madrid , Plaza de Ciencias 3 , Madrid , 28040 , Madrid , Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de An\u00e1lisis Matem\u00e1tico y Matem\u00e1tica Aplicada , Universidad Complutense de Madrid , Plaza de Ciencias 3 , Madrid , 28040 , Madrid , Spain","institution_ids":["https://openalex.org/I121748325"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041065153","display_name":"Leandro M. Del Pezzo","orcid":"https://orcid.org/0000-0002-5263-3446","observed_orcids":["https://orcid.org/0000-0002-5263-3446"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Del Pezzo, Leandro M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9961000084877014,"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"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9961000084877014,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.0012000000569969416,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.00039999998989515007,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/moving-plane-method","display_name":"moving plane method","score":0.9610000252723694},{"id":"https://openalex.org/keywords/fractional-laplacian","display_name":"fractional Laplacian","score":0.9419999718666077},{"id":"https://openalex.org/keywords/quenching","display_name":"quenching","score":0.8360000252723694},{"id":"https://openalex.org/keywords/parabolic-systems","display_name":"parabolic systems","score":0.7580000162124634},{"id":"https://openalex.org/keywords/global-existence","display_name":"global existence","score":0.7269999980926514}],"concepts":[{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7477999925613403},{"id":"https://openalex.org/C121745418","wikidata":"https://www.wikidata.org/wiki/Q585536","display_name":"Quenching (fluorescence)","level":3,"score":0.6647999882698059},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.638700008392334},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6078000068664551},{"id":"https://openalex.org/C58754882","wikidata":"https://www.wikidata.org/wiki/Q1502887","display_name":"Geodetic datum","level":2,"score":0.4544000029563904},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4447999894618988},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4359999895095825},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.42570000886917114},{"id":"https://openalex.org/C125287762","wikidata":"https://www.wikidata.org/wiki/Q1758948","display_name":"Absorption (acoustics)","level":2,"score":0.41749998927116394},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.3968000113964081},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.3361000120639801},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28630000352859497},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.2806999981403351},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.25440001487731934},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.08014","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08014","pdf_url":"https://arxiv.org/pdf/2610.08014","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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.2610.08014","doi":"https://doi.org/10.48550/arxiv.2610.08014","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.08014","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.08014","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08014","pdf_url":"https://arxiv.org/pdf/2610.08014","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G103507813","display_name":null,"funder_award_id":"MCIU/AEI/ 10.13039/501100011033","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G1105844351","display_name":null,"funder_award_id":"10.13039.501100011033","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G1272900390","display_name":null,"funder_award_id":"PID2023","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G1754140167","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320310753","funder_display_name":"Agencia Nacional de Investigaci\u00f3n e Innovaci\u00f3n"},{"id":"https://openalex.org/G1787261173","display_name":null,"funder_award_id":"PID2023-148028NB-I00","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G2019505627","display_name":null,"funder_award_id":"MCIU/AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G410571670","display_name":null,"funder_award_id":"10.13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G4212894969","display_name":null,"funder_award_id":"PID2022","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G451917667","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G491712853","display_name":null,"funder_award_id":"/ AEI10.13039/501100011033","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G5539308778","display_name":null,"funder_award_id":"AEI/10.13039/501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G5635532810","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G5967599077","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335322","funder_display_name":"European Regional Development Fund"},{"id":"https://openalex.org/G7805626310","display_name":null,"funder_award_id":"10.13039","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G7863371703","display_name":null,"funder_award_id":".13039/501100011033","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"},{"id":"https://openalex.org/G8497050386","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320315062","funder_display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades"}],"funders":[{"id":"https://openalex.org/F4320310753","display_name":"Agencia Nacional de Investigaci\u00f3n e Innovaci\u00f3n","ror":"https://ror.org/03egaj678"},{"id":"https://openalex.org/F4320315062","display_name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","ror":null},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":"https://ror.org/003x0zc53"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220919403.pdf","grobid_xml":"https://content.openalex.org/works/W7220919403.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1970612773","https://openalex.org/W1975536006","https://openalex.org/W1982071274","https://openalex.org/W1985307318","https://openalex.org/W2016697490","https://openalex.org/W2040223941","https://openalex.org/W2048891896","https://openalex.org/W2054760717","https://openalex.org/W2084178613","https://openalex.org/W2086652030","https://openalex.org/W2092194892","https://openalex.org/W2095108429","https://openalex.org/W2130440873","https://openalex.org/W2152284775","https://openalex.org/W2171707956","https://openalex.org/W2293368161","https://openalex.org/W2963855588","https://openalex.org/W3027026734","https://openalex.org/W3133606445","https://openalex.org/W3152207607","https://openalex.org/W4213341209","https://openalex.org/W4403403373","https://openalex.org/W4417054405","https://openalex.org/W4417457272","https://openalex.org/W7220735270"],"related_works":["https://openalex.org/W4417054405","https://openalex.org/W2040223941","https://openalex.org/W2152284775","https://openalex.org/W4391984169","https://openalex.org/W2890109250","https://openalex.org/W4417457272","https://openalex.org/W2790323524","https://openalex.org/W2373673682","https://openalex.org/W2150756909","https://openalex.org/W1579506470"],"abstract_inverted_index":{"In":[0],"this":[1,41],"paper":[2],"we":[3],"develop":[4],"a":[5,17,53,66,86,117],"parabolic":[6],"version":[7],"of":[8,11,57,68,120],"the":[9,34,45,58,93,102,110,121],"method":[10],"moving":[12],"planes":[13],"on":[14],"systems":[15,51],"with":[16,52],"mixed":[18],"local":[19],"and":[20,77],"nonlocal":[21],"diffusion":[22],"operator,":[23],"that":[24,63,78,101],"being":[25],"$\\mathcal{L}":[26],"=":[27],"-(-\u0394)^s":[28],"+":[29],"\u0394$,":[30],"where":[31],"$(-\u0394)^s$":[32],"is":[33,95],"integral":[35],"fractional":[36],"laplacian.":[37],"We":[38,61,98],"then":[39],"use":[40],"result":[42],"to":[43,109],"study":[44],"quenching":[46,103],"phenomena":[47,104],"occurring":[48],"in":[49,116],"said":[50],"singular":[54],"absorption":[55],"term":[56],"type":[59],"$(1-u)^{-p}$.":[60],"prove":[62,100],"there":[64,84],"exists":[65,85],"range":[67],"multiplicative":[69,89],"parameters":[70],"for":[71,79],"which":[72],"every":[73],"solution":[74,94],"presents":[75],"quenching,":[76],"any":[80],"initial":[81],"datum":[82],"$u_0$,":[83],"small":[87],"enough":[88],"parameter":[90],"such":[91],"as":[92],"globally":[96],"defined.":[97],"also":[99],"cannot":[105],"happen":[106],"arbitrarily":[107],"close":[108],"boundary,":[111],"but":[112],"they":[113],"are":[114],"contained":[115],"compact":[118],"subset":[119],"domain.":[122]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}