{"id":"https://openalex.org/W6929330724","doi":"https://doi.org/10.48550/arxiv.2503.13922","title":"Existence and Smoothing for a Nondivergence-Form Degenerate Diffusion from Plasma-Wave Theory","display_name":"Existence and Smoothing for a Nondivergence-Form Degenerate Diffusion from Plasma-Wave Theory","publication_year":2025,"publication_date":"2025-03-18","ids":{"openalex":"https://openalex.org/W6929330724","doi":"https://doi.org/10.48550/arxiv.2503.13922"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2503.13922","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2503.13922","pdf_url":"https://arxiv.org/pdf/2503.13922","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/2503.13922","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Porteous, William","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Porteous, William","raw_affiliation_strings":["Department of Mathematics , The University of Texas at Austin , 2515 Speedway , PMA 8.100 , Austin , TX 78712 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , The University of Texas at Austin , 2515 Speedway , PMA 8.100 , Austin , TX 78712 , USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087543049","display_name":"Irene M. Gamba","orcid":"https://orcid.org/0000-0002-4956-2376","observed_orcids":["https://orcid.org/0000-0002-4956-2376"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gamba, Irene M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5127344358","display_name":"Kun Huang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Huang, Kun","raw_affiliation_strings":["Department of Mathematics , The University of Texas at Austin , 2515 Speedway , PMA 8.100 , Austin , TX 78712 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , The University of Texas at Austin , 2515 Speedway , PMA 8.100 , Austin , TX 78712 , USA","institution_ids":["https://openalex.org/I86519309"]}]}],"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":true,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.7851999998092651,"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":0.7851999998092651,"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":0.1136000007390976,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.031099999323487282,"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/degenerate-parabolic-equations","display_name":"degenerate parabolic equations","score":0.9160000085830688},{"id":"https://openalex.org/keywords/weak-solutions","display_name":"weak solutions","score":0.7300000190734863},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.6050000190734863},{"id":"https://openalex.org/keywords/plasma-waves","display_name":"plasma waves","score":0.6600000262260437},{"id":"https://openalex.org/keywords/electron-distribution-function","display_name":"electron distribution function","score":0.6930000185966492},{"id":"https://openalex.org/keywords/spectral-energy-density","display_name":"spectral energy density","score":0.9570000171661377},{"id":"https://openalex.org/keywords/cauchy-dirichlet-problem","display_name":"Cauchy-Dirichlet problem","score":0.843999981880188},{"id":"https://openalex.org/keywords/holder-regularity","display_name":"H\u00f6lder regularity","score":0.7279999852180481},{"id":"https://openalex.org/keywords/mass-conservation","display_name":"mass conservation","score":0.5509999990463257}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6654999852180481},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5674999952316284},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5462999939918518},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5428000092506409},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.5295000076293945},{"id":"https://openalex.org/C82706917","wikidata":"https://www.wikidata.org/wiki/Q10251","display_name":"Plasma","level":2,"score":0.49559998512268066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.453000009059906},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.3968000113964081},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.3882000148296356},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.384799987077713},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.3659999966621399},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C2778190657","wikidata":"https://www.wikidata.org/wiki/Q16956934","display_name":"Plasma diffusion","level":3,"score":0.3402999937534332},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3391999900341034},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2903999984264374},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.27410000562667847},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.2533999979496002},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2503.13922","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2503.13922","pdf_url":"https://arxiv.org/pdf/2503.13922","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.2503.13922","doi":"https://doi.org/10.48550/arxiv.2503.13922","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2503.13922","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2503.13922","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2503.13922","pdf_url":"https://arxiv.org/pdf/2503.13922","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":[],"sustainable_development_goals_aurora":[{"score":0.5439736247062683,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"study_designs":[],"awards":[{"id":"https://openalex.org/G3216784629","display_name":"Collisional Kinetic Transport: Analysis and Numerical Methods","funder_award_id":"2009736","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G572320215","display_name":"RTG: Analysis of Partial Differential Equations","funder_award_id":"1840314","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5786956723","display_name":"Kinetic Transport of Interactive Complex Particle Dynamics in Mean Fields.","funder_award_id":"2408263","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6868596310","display_name":"SIMULATION CENTER FOR RUNAWAY ELECTRON AVOIDANCE AND MITIGATION","funder_award_id":"DESC0016283","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W6929330724.pdf","grobid_xml":"https://content.openalex.org/works/W6929330724.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,122],"prove":[1,182],"existence,":[2],"positive-time":[3,224],"smoothing,":[4],"and":[5,37,96,109,149,151,203,214,233],"physical":[6,106],"admissibility":[7],"of":[8,50,57,70,114,198],"weak":[9,89,196],"solutions":[10,90],"to":[11,74,164,236],"the":[12,29,35,48,54,61,84,100,105,112,115,129,142,173,184,199,207,215,221],"degenerate":[13],"parabolic":[14,125],"Cauchy-Dirichlet":[15],"problem":[16,43,86],"$\\partial_t":[17,136],"u":[18,21,23],"=":[19],"\u03c1_\u03bb(x)":[20,25],"\\partial_x^2":[22],"+":[24],"g(x)":[26],"u$":[27],"on":[28,135,206],"half-line,":[30],"where":[31],"$\u03c1_\u03bb$":[32],"vanishes":[33],"at":[34,39,156,230],"boundary":[36],"grows":[38],"infinity.":[40],"This":[41,64,159],"scalar":[42,85,185],"arises":[44],"by":[45,53,167],"formally":[46],"reducing":[47],"system":[49,175],"equations":[51],"given":[52],"quasilinear":[55,174],"theory":[56,65],"plasma":[58],"waves":[59],"in":[60,147,154],"one-dimensional":[62],"case.":[63],"models":[66],"a":[67,75,124,188,195,237,244],"background":[68],"distribution":[69],"electrons":[71],"$f$":[72],"coupled":[73],"spectral":[76],"energy":[77],"density":[78],"$W$":[79],"through":[80],"wave-particle":[81],"resonance.":[82],"For":[83],"we":[87,171,181],"construct":[88],"from":[91,138],"weighted":[92],"$L^p$":[93],"initial":[94,208,216],"data":[95,103],"bounded":[97,239],"reaction,":[98],"admitting":[99],"unbounded,":[101],"discontinuous":[102],"that":[104,183],"model":[107],"demands,":[108],"lying":[110],"beyond":[111],"reach":[113],"continuous-data":[116],"theories":[117],"developed":[118],"for":[119,128],"nearby":[120],"problems.":[121],"identify":[123],"smoothing":[126,235],"effect":[127],"constructed":[130],"solution,":[131],"namely":[132],"one-sided":[133],"bounds":[134],"u$:":[137],"merely":[139],"integrable":[140],"data,":[141,209],"solution":[143,186,197],"becomes":[144],"locally":[145,152,238],"H\u00f6lder":[146],"space":[148,155],"time":[150],"Lipschitz":[153],"positive":[157],"times.":[158],"spatial":[160],"regularity":[161],"is":[162,194,218],"shown":[163],"be":[165],"sharp":[166],"explicit":[168],"examples.":[169],"Finally,":[170],"address":[172],"itself,":[176],"whose":[177],"well-posedness":[178],"remains":[179],"open:":[180],"induces":[187],"particle-wave":[189],"pair":[190,222],"$(f^{\\ast},":[191],"W^{\\ast})$":[192],"which":[193],"system.":[200],"Under":[201],"nonnegativity":[202],"finite-moment":[204],"hypotheses":[205],"both":[210],"components":[211],"remain":[212],"nonnegative":[213],"mass":[217],"conserved.":[219],"Moreover,":[220],"inherits":[223],"regularity,":[225],"with":[226],"$W^{\\ast}$":[227],"decaying":[228],"quantitatively":[229],"large":[231],"wavenumber":[232],"$f^{\\ast}$":[234],"function":[240],"even":[241],"when":[242],"initially":[243],"measure.":[245]},"counts_by_year":[],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}