{"id":"https://openalex.org/W7214349443","doi":"https://doi.org/10.48550/arxiv.2609.29883","title":"Existence and uniqueness of global weak solutions to degenerate volume-filling chemotaxis systems with source terms","display_name":"Existence and uniqueness of global weak solutions to degenerate volume-filling chemotaxis systems with source terms","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214349443","doi":"https://doi.org/10.48550/arxiv.2609.29883"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.29883","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29883","pdf_url":"https://arxiv.org/pdf/2609.29883","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/2609.29883","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132661536","display_name":"Osuke Shibata","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Shibata, Osuke","raw_affiliation_strings":["Department of Mathematics , Tokyo University of Science 1-3 , Kagurazaka , Shinjuku-ku , Tokyo 162-8601 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Tokyo University of Science 1-3 , Kagurazaka , Shinjuku-ku , Tokyo 162-8601 , Japan","institution_ids":["https://openalex.org/I161296585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5132661536"],"corresponding_institution_ids":["https://openalex.org/I161296585"],"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9970999956130981,"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":0.9970999956130981,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.001500000013038516,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","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/global-weak-solutions","display_name":"global weak solutions","score":0.9890000224113464},{"id":"https://openalex.org/keywords/uniqueness-of-weak-solutions","display_name":"uniqueness of weak solutions","score":0.8759999871253967},{"id":"https://openalex.org/keywords/zero-flux-boundary-conditions","display_name":"no-flux boundary conditions","score":0.7400000095367432},{"id":"https://openalex.org/keywords/bounded-domains","display_name":"bounded domains","score":0.718999981880188},{"id":"https://openalex.org/keywords/degenerate-diffusion","display_name":"degenerate diffusion","score":0.48500001430511475}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8910999894142151},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.8198999762535095},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.7580000162124634},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6751999855041504},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5720999836921692},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.41830000281333923},{"id":"https://openalex.org/C54166955","wikidata":"https://www.wikidata.org/wiki/Q658145","display_name":"Chemotaxis","level":3,"score":0.39570000767707825},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3767000138759613},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3158999979496002},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.29883","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29883","pdf_url":"https://arxiv.org/pdf/2609.29883","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.2609.29883","doi":"https://doi.org/10.48550/arxiv.2609.29883","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.29883","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:2609.29883","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29883","pdf_url":"https://arxiv.org/pdf/2609.29883","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214349443.pdf","grobid_xml":"https://content.openalex.org/works/W7214349443.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7153293608"],"related_works":["https://openalex.org/W7153293608","https://openalex.org/W1977999792","https://openalex.org/W7222084038","https://openalex.org/W2290971940","https://openalex.org/W153626043","https://openalex.org/W3028335581","https://openalex.org/W2788247819","https://openalex.org/W3014354379","https://openalex.org/W4383032171","https://openalex.org/W2504708259"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,58,104],"concerned":[3],"with":[4,16,83,94],"a":[5,48,88],"no-flux":[6],"initial-boundary":[7],"value":[8],"problem":[9],"for":[10,76,110],"the":[11],"degenerate":[12],"volume-filling":[13],"chemotaxis":[14],"system":[15],"source":[17],"terms,":[18],"\\begin{align*}":[19],"u_t":[20],"=":[21,37,72,74,108],"\\nabla":[22,25,29],"\\cdot":[23],"(D(u,v)":[24],"u":[26],"-":[27],"h(u,v)":[28],"v)":[30],"+":[31,39],"f(x,":[32],"u,":[33],"v),":[34],"\\quad":[35,41],"v_t":[36],"\u0394v":[38],"g(u,v),":[40],"x\\in":[42],"\u03a9,":[43],"\\":[44],"t>0":[45],"\\end{align*}":[46],"in":[47],"smoothly":[49],"bounded":[50],"domain":[51],"$\u03a9\\subset":[52],"\\mathbb{R}^N$":[53],"$(N":[54],"\\in":[55],"\\mathbb{N})$.":[56],"It":[57],"shown":[59],"that":[60],"when":[61,106],"$D$,":[62,116],"$h$,":[63,117],"$f$":[64],"and":[65,81,113,115,120],"$g$":[66,119],"satisfy":[67,125],"suitable":[68],"assumptions":[69],"involving":[70],"$D(1,\\cdot)=h(0,\\cdot)=h(1,\\cdot)=f(\\cdot,0,\\cdot)":[71],"f(\\cdot,1,\\cdot)":[73],"0$,":[75],"nonnegative":[77],"initial":[78],"data":[79],"$u_0$":[80],"$v_0$":[82,121],"$u_0\\le":[84],"1$,":[85],"there":[86],"exists":[87],"global":[89,101],"weak":[90,102],"solution":[91],"$(u,":[92],"v)$":[93],"$u\\le":[95],"1$.":[96],"In":[97],"addition,":[98],"uniqueness":[99],"of":[100],"solutions":[103],"established":[105],"$D(r,s)":[107],"D(r)$":[109],"all":[111],"$r\\in[0,1]$":[112],"$s\\in[0,\\infty)$,":[114],"$f$,":[118],"are":[122],"supposed":[123],"to":[124],"additional":[126],"conditions.":[127]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-26T00:00:00"}