{"id":"https://openalex.org/W2008702562","doi":"https://doi.org/10.1137/090774495","title":"Self-Similar Blowup Solutions to an Aggregation Equation in $R^n$","display_name":"Self-Similar Blowup Solutions to an Aggregation Equation in $R^n$","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2008702562","doi":"https://doi.org/10.1137/090774495","mag":"2008702562"},"language":"en","primary_location":{"id":"doi:10.1137/090774495","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090774495","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072428176","display_name":"Yanghong Huang","orcid":"https://orcid.org/0000-0003-4145-6621"},"institutions":[{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yanghong Huang","raw_affiliation_strings":["Applied Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Mathematics","institution_ids":["https://openalex.org/I4210131439"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090707978","display_name":"Andrea L. Bertozzi","orcid":"https://orcid.org/0000-0003-0396-7391"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrea L. Bertozzi","raw_affiliation_strings":["Department of Mathematics, UCLA, Los Angeles, CA 90095"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, UCLA, Los Angeles, CA 90095","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.398,"has_fulltext":false,"cited_by_count":69,"citation_normalized_percentile":{"value":0.93691648,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"70","issue":"7","first_page":"2582","last_page":"2603"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9983000159263611,"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":0.9983000159263611,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/nabla-symbol","display_name":"Nabla symbol","score":0.8551113605499268},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.7574781179428101},{"id":"https://openalex.org/keywords/self-similarity","display_name":"Self-similarity","score":0.6781444549560547},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.63539057970047},{"id":"https://openalex.org/keywords/similarity-solution","display_name":"Similarity solution","score":0.6233582496643066},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5427617430686951},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.5239893794059753},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47700953483581543},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4269932508468628},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3901197910308838},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3676930069923401},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3519894480705261},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2468835711479187},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12024939060211182},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.11974197626113892},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07826831936836243},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.058177828788757324},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.0560002326965332},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.055626094341278076}],"concepts":[{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.8551113605499268},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.7574781179428101},{"id":"https://openalex.org/C119453123","wikidata":"https://www.wikidata.org/wiki/Q262372","display_name":"Self-similarity","level":2,"score":0.6781444549560547},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.63539057970047},{"id":"https://openalex.org/C2777282005","wikidata":"https://www.wikidata.org/wiki/Q4056366","display_name":"Similarity solution","level":3,"score":0.6233582496643066},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5427617430686951},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.5239893794059753},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47700953483581543},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4269932508468628},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3901197910308838},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3676930069923401},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3519894480705261},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2468835711479187},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12024939060211182},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.11974197626113892},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07826831936836243},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.058177828788757324},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.0560002326965332},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.055626094341278076},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C111603439","wikidata":"https://www.wikidata.org/wiki/Q752193","display_name":"Boundary layer","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/090774495","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090774495","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/bfc1a53e-aa88-4042-9fa2-c7da649ed4aa","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/bfc1a53e-aa88-4042-9fa2-c7da649ed4aa","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Huang, Y & Bertozzi, A L 2010, 'Self-similar blowup solutions to an aggregation equation in {$\\bold R^n$}', SIAM J. Appl. Math., vol. 70, no. 7, pp. 2582-2603. https://doi.org/10.1137/090774495","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.186.1855","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.186.1855","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucla.edu/%7Ebertozzi/papers/SIAP10.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.711.6666","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.711.6666","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://personalpages.manchester.ac.uk/staff/yanghong.huang/paper/simiblowup.pdf","raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:publications/bfc1a53e-aa88-4042-9fa2-c7da649ed4aa","is_oa":false,"landing_page_url":"https://www.research.manchester.ac.uk/portal/en/publications/selfsimilar-blowup-solutions-to-an-aggregation-equation-in-bold-rn(bfc1a53e-aa88-4042-9fa2-c7da649ed4aa).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Huang, Y & Bertozzi, A L 2010, 'Self-similar blowup solutions to an aggregation equation in {$\\bold R^n$}', SIAM J. Appl. Math., vol. 70, no. 7, pp. 2582-2603. https://doi.org/10.1137/090774495","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G121431729","display_name":"Dynamics of aggregation and collapse in multidimensional swarming models","funder_award_id":"0907931","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W1486027622","https://openalex.org/W1510464068","https://openalex.org/W1558066780","https://openalex.org/W1565688698","https://openalex.org/W1963640358","https://openalex.org/W1963810041","https://openalex.org/W1970414832","https://openalex.org/W1970658847","https://openalex.org/W1973034834","https://openalex.org/W1974612778","https://openalex.org/W1978507854","https://openalex.org/W1984878971","https://openalex.org/W1987307083","https://openalex.org/W1991440858","https://openalex.org/W1994909631","https://openalex.org/W2000382398","https://openalex.org/W2001354695","https://openalex.org/W2006078471","https://openalex.org/W2026873879","https://openalex.org/W2027481868","https://openalex.org/W2027880032","https://openalex.org/W2031055103","https://openalex.org/W2040910471","https://openalex.org/W2042119318","https://openalex.org/W2042892258","https://openalex.org/W2044580900","https://openalex.org/W2048810410","https://openalex.org/W2049561031","https://openalex.org/W2049966323","https://openalex.org/W2052946502","https://openalex.org/W2054363690","https://openalex.org/W2061507957","https://openalex.org/W2076068357","https://openalex.org/W2078393946","https://openalex.org/W2090935337","https://openalex.org/W2094820190","https://openalex.org/W2105835312","https://openalex.org/W2119414533","https://openalex.org/W2121676742","https://openalex.org/W2135138457","https://openalex.org/W2140443109","https://openalex.org/W2147500254","https://openalex.org/W2155385278","https://openalex.org/W2156934943","https://openalex.org/W2158215874","https://openalex.org/W2160964994","https://openalex.org/W2164829730","https://openalex.org/W2171306535","https://openalex.org/W2285847518","https://openalex.org/W2390063579","https://openalex.org/W4232571383"],"related_works":["https://openalex.org/W1917482396","https://openalex.org/W3092805691","https://openalex.org/W1992569581","https://openalex.org/W2485086906","https://openalex.org/W2008702562","https://openalex.org/W1994032359","https://openalex.org/W2054417241","https://openalex.org/W2056111788","https://openalex.org/W2991040229","https://openalex.org/W1999042108"],"abstract_inverted_index":{"We":[0],"present":[1],"numerical":[2],"simulations":[3],"of":[4,22],"radially":[5],"symmetric":[6],"finite":[7],"time":[8],"blowup":[9,24,38],"for":[10,45],"the":[11,17,23,34,37,61],"aggregation":[12],"equation":[13],"$u_t=\\nabla\\cdot(u\\nabla":[14],"K*u)$,":[15],"where":[16],"kernel":[18],"$K(x)=|x|$.":[19],"The":[20],"dynamics":[21],"exhibits":[25,63],"self-similar":[26],"behavior":[27],"in":[28,43],"which":[29],"zero":[30],"mass":[31],"concentrates":[32],"at":[33,36],"core":[35],"time.":[39],"Computations":[40],"are":[41],"performed":[42],"$R^n$":[44],"n":[46],"between":[47],"2":[48],"and":[49],"10":[50],"using":[51],"a":[52],"method":[53],"based":[54],"on":[55],"characteristics.":[56],"In":[57],"all":[58],"cases":[59],"studied,":[60],"self-similarity":[62],"second-kind":[64],"(anomalous)":[65],"scaling.":[66]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
