{"id":"https://openalex.org/W2157786389","doi":"https://doi.org/10.1007/0-387-33006-2_5","title":"Analysis of a PDE Model for Sandpile Growth","display_name":"Analysis of a PDE Model for Sandpile Growth","publication_year":2006,"publication_date":"2006-06-07","ids":{"openalex":"https://openalex.org/W2157786389","doi":"https://doi.org/10.1007/0-387-33006-2_5","mag":"2157786389"},"language":"en","primary_location":{"id":"doi:10.1007/0-387-33006-2_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/0-387-33006-2_5","pdf_url":"https://link.springer.com/content/pdf/10.1007/0-387-33006-2_5.pdf","source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/0-387-33006-2_5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049253329","display_name":"Piermarco Cannarsa","orcid":"https://orcid.org/0000-0003-2576-2004"},"institutions":[{"id":"https://openalex.org/I116067653","display_name":"University of Rome Tor Vergata","ror":"https://ror.org/02p77k626","country_code":"IT","type":"education","lineage":["https://openalex.org/I116067653"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"P. Cannarsa","raw_affiliation_strings":["Department of Mathematics, University of Rome \u201cTor Vergata\u201d, Rome, Italy","Department of Mathematics, University of Rome \"Tor Vergata\", Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Rome \u201cTor Vergata\u201d, Rome, Italy","institution_ids":["https://openalex.org/I116067653"]},{"raw_affiliation_string":"Department of Mathematics, University of Rome \"Tor Vergata\", Rome, Italy","institution_ids":["https://openalex.org/I116067653"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5049253329"],"corresponding_institution_ids":["https://openalex.org/I116067653"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20973783,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"41","last_page":"50"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9997000098228455,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9997000098228455,"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/T12351","display_name":"Geometry and complex manifolds","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.984000027179718,"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/mathematics","display_name":"Mathematics","score":0.705463707447052},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5682838559150696},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5495622158050537},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5328235030174255},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4629304111003876},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4543262720108032},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4234580397605896},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4106951355934143},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.32755380868911743},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2126598060131073}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.705463707447052},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5682838559150696},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5495622158050537},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5328235030174255},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4629304111003876},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4543262720108032},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4234580397605896},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4106951355934143},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.32755380868911743},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2126598060131073}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/0-387-33006-2_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/0-387-33006-2_5","pdf_url":"https://link.springer.com/content/pdf/10.1007/0-387-33006-2_5.pdf","source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/0-387-33006-2_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/0-387-33006-2_5","pdf_url":"https://link.springer.com/content/pdf/10.1007/0-387-33006-2_5.pdf","source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2157786389.pdf","grobid_xml":"https://content.openalex.org/works/W2157786389.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W99137304","https://openalex.org/W1494380031","https://openalex.org/W1531971668","https://openalex.org/W1544592589","https://openalex.org/W1596052672","https://openalex.org/W1732289946","https://openalex.org/W1971242648","https://openalex.org/W1994571215","https://openalex.org/W1995014297","https://openalex.org/W1995873164","https://openalex.org/W1999112138","https://openalex.org/W2002687104","https://openalex.org/W2040436503","https://openalex.org/W2044305163","https://openalex.org/W2045019334","https://openalex.org/W2046571480","https://openalex.org/W2053299708","https://openalex.org/W2056316058","https://openalex.org/W2092981999","https://openalex.org/W2127065532","https://openalex.org/W2142056719","https://openalex.org/W2160273864","https://openalex.org/W2309419782","https://openalex.org/W2319915396"],"related_works":["https://openalex.org/W3013085049","https://openalex.org/W55883722","https://openalex.org/W1560496689","https://openalex.org/W1992739770","https://openalex.org/W2394379345","https://openalex.org/W2999616507","https://openalex.org/W4392238179","https://openalex.org/W3164276969","https://openalex.org/W2029287765","https://openalex.org/W2043671984"],"abstract_inverted_index":{"In":[0],"the":[1,7,14,36,72,76,90,95,100,104],"dynamical":[2],"theory":[3],"of":[4,16,19,35,54,60,78,94,99,107],"granular":[5],"matter,":[6],"so-called":[8],"table":[9,37],"problem":[10,50],"consists":[11],"in":[12,92],"studying":[13],"evolution":[15],"a":[17,24,47,52,62],"heap":[18],"matter":[20],"poured":[21],"continuously":[22],"onto":[23],"bounded":[25],"domain":[26],"\u03a9":[27],"\u2282":[28],"R":[29],"2":[30],".":[31],"The":[32,58],"mathematical":[33,68],"description":[34],"problem,":[38,74],"at":[39],"an":[40,85],"equilibrium":[41],"configuration,":[42],"can":[43],"be":[44],"reduced":[45],"to":[46,103],"boundary":[48,96],"value":[49],"for":[51,89],"system":[53],"partial":[55],"differential":[56],"equations.":[57],"analysis":[59],"such":[61,70],"system,":[63],"also":[64],"connected":[65],"with":[66],"other":[67],"models":[69],"as":[71],"Monge-Kantorovich":[73],"is":[75,84],"object":[77],"this":[79],"paper.":[80],"Our":[81],"main":[82],"result":[83],"integral":[86],"representation":[87],"formula":[88],"solution,":[91],"terms":[93],"curvature":[97],"and":[98],"normal":[101],"distance":[102],"cut":[105],"locus":[106],"\u03a9.":[108]},"counts_by_year":[],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
