{"id":"https://openalex.org/W7224949533","doi":"https://doi.org/10.48550/arxiv.2610.39166","title":"On the well-posedness of a certain model with mixed diffusion appearing in the mathematical biology","display_name":"On the well-posedness of a certain model with mixed diffusion appearing in the mathematical biology","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224949533","doi":"https://doi.org/10.48550/arxiv.2610.39166"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.39166","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39166","pdf_url":"https://arxiv.org/pdf/2610.39166","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.39166","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108256376","display_name":"Messoud A. Efendiev","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3018134672","display_name":"Helmholtz Munich","ror":"https://ror.org/00cfam450","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I3018134672"]},{"id":"https://openalex.org/I4210127900","display_name":"Azerbaijan University of Architecture and Construction","ror":"https://ror.org/02shm3a27","country_code":"AZ","type":"education","lineage":["https://openalex.org/I4210127900"]}],"countries":["AZ","DE"],"is_corresponding":false,"raw_author_name":"Efendiev, Messoud","raw_affiliation_strings":["Azerbaijan University of Architecture and Construction , Baku , Azerbaijan","Helmholtz Zentrum M\u00fcnchen , Institut f\u00fcr Computational Biology , Ingolst\u00e4dter Landstrasse 1 Neuherberg , 85764 , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Azerbaijan University of Architecture and Construction , Baku , Azerbaijan","institution_ids":["https://openalex.org/I4210127900"]},{"raw_affiliation_string":"Helmholtz Zentrum M\u00fcnchen , Institut f\u00fcr Computational Biology , Ingolst\u00e4dter Landstrasse 1 Neuherberg , 85764 , Germany","institution_ids":["https://openalex.org/I3018134672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075805405","display_name":"Vitali Vougalter","orcid":"https://orcid.org/0000-0001-7403-3444","observed_orcids":["https://orcid.org/0000-0001-7403-3444"]},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Vougalter, Vitali","raw_affiliation_strings":["Department of Mathematics , University of Toronto Toronto , Ontario , M5S 2E4 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Toronto Toronto , Ontario , M5S 2E4 , Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.7235999703407288,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.7235999703407288,"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":0.13269999623298645,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.07680000364780426,"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/global-well-posedness","display_name":"global well-posedness","score":0.9559999704360962},{"id":"https://openalex.org/keywords/integro-differential-equations","display_name":"integro-differential equations","score":0.8610000014305115},{"id":"https://openalex.org/keywords/mixed-diffusion","display_name":"mixed diffusion","score":0.9359999895095825},{"id":"https://openalex.org/keywords/fractional-laplacian","display_name":"fractional Laplacian","score":0.9940000176429749},{"id":"https://openalex.org/keywords/laplacian","display_name":"Laplacian","score":0.7889999747276306},{"id":"https://openalex.org/keywords/drift-term","display_name":"drift term","score":0.9829999804496765},{"id":"https://openalex.org/keywords/cell-population-dynamics","display_name":"cell population dynamics","score":0.8930000066757202},{"id":"https://openalex.org/keywords/fixed-point-technique","display_name":"fixed point approach","score":0.5950000286102295},{"id":"https://openalex.org/keywords/two-dimensional-space","display_name":"two-dimensional space","score":0.40799999237060547}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5814999938011169},{"id":"https://openalex.org/C20129857","wikidata":"https://www.wikidata.org/wiki/Q751611","display_name":"Mathematical and theoretical biology","level":2,"score":0.5232999920845032},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.5174999833106995},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5008999705314636},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.47279998660087585},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4717000126838684},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.45750001072883606},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4406000077724457},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.43869999051094055},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43639999628067017},{"id":"https://openalex.org/C2779193601","wikidata":"https://www.wikidata.org/wiki/Q20026918","display_name":"Mathematical theory","level":2,"score":0.40059998631477356},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.3977999985218048},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37450000643730164},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3736000061035156},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36579999327659607},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.3619000017642975},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.3517000079154968},{"id":"https://openalex.org/C52079815","wikidata":"https://www.wikidata.org/wiki/Q7229808","display_name":"Population model","level":3,"score":0.3327000141143799},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.30379998683929443},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C206743973","wikidata":"https://www.wikidata.org/wiki/Q178377","display_name":"Mathematical induction","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.2574999928474426},{"id":"https://openalex.org/C70615421","wikidata":"https://www.wikidata.org/wiki/Q339444","display_name":"Laplace's equation","level":3,"score":0.25429999828338623}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.39166","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39166","pdf_url":"https://arxiv.org/pdf/2610.39166","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.2610.39166","doi":"https://doi.org/10.48550/arxiv.2610.39166","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.39166","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.39166","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.39166","pdf_url":"https://arxiv.org/pdf/2610.39166","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224949533.pdf","grobid_xml":"https://content.openalex.org/works/W7224949533.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4402696692","https://openalex.org/W4415671286","https://openalex.org/W4416053708","https://openalex.org/W7128467880","https://openalex.org/W2006078471","https://openalex.org/W2125225054","https://openalex.org/W2605687023","https://openalex.org/W2074718512","https://openalex.org/W4322581913","https://openalex.org/W2885904183"],"abstract_inverted_index":{"The":[0,65],"work":[1],"deals":[2],"with":[3],"establishing":[4],"the":[5,9,14,18,24,27,31,39,46,49,57,62],"global":[6],"well-posedness":[7],"in":[8,17,23,35,42,45,61],"space":[10,19],"$W^{(1,2),2}(R^{2}\\times":[11],"R^{+})$":[12],"of":[13,20,48],"integro-differential":[15],"equation":[16],"two":[21],"dimensions":[22],"situation":[25],"when":[26],"diffusion":[28],"term":[29],"involves":[30],"standard":[32],"Laplace":[33],"operator":[34],"one":[36],"direction":[37,44],"and":[38],"fractional":[40],"Laplacian":[41],"another":[43],"presence":[47],"drift":[50],"term.":[51],"Such":[52],"model":[53],"is":[54,67],"relevant":[55],"to":[56],"cell":[58],"population":[59],"dynamics":[60],"Mathematical":[63],"Biology.":[64],"proof":[66],"based":[68],"on":[69],"a":[70],"fixed":[71],"point":[72],"technique.":[73]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-31T00:00:00"}
