{"id":"https://openalex.org/W2008358701","doi":"https://doi.org/10.1090/s0025-5718-00-01254-0","title":"Existence of discrete shock profiles of a class of monotonicity preserving schemes for conservation laws","display_name":"Existence of discrete shock profiles of a class of monotonicity preserving schemes for conservation laws","publication_year":2000,"publication_date":"2000-05-23","ids":{"openalex":"https://openalex.org/W2008358701","doi":"https://doi.org/10.1090/s0025-5718-00-01254-0","mag":"2008358701"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01254-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01254-0","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01254-0/S0025-5718-00-01254-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01254-0/S0025-5718-00-01254-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037891818","display_name":"Haitao Fan","orcid":"https://orcid.org/0000-0002-5821-9609"},"institutions":[{"id":"https://openalex.org/I184565670","display_name":"Georgetown University","ror":"https://ror.org/05vzafd60","country_code":"US","type":"education","lineage":["https://openalex.org/I184565670"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Haitao Fan","raw_affiliation_strings":["Department of Mathematics, Georgetown University, Washington, DC 20057","Department of Mathematics, Georgetown University, Washington, DC, 20057"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Georgetown University, Washington, DC 20057","institution_ids":["https://openalex.org/I184565670"]},{"raw_affiliation_string":"Department of Mathematics, Georgetown University, Washington, DC, 20057","institution_ids":["https://openalex.org/I184565670"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037891818"],"corresponding_institution_ids":["https://openalex.org/I184565670"],"apc_list":null,"apc_paid":null,"fwci":0.5541,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.67113695,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"70","issue":"235","first_page":"1043","last_page":"1069"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9993000030517578,"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":0.9975000023841858,"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/conservation-law","display_name":"Conservation law","score":0.9126816987991333},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8550633192062378},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6691397428512573},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.6185640096664429},{"id":"https://openalex.org/keywords/shock","display_name":"Shock (circulatory)","score":0.5242859721183777},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5191358923912048},{"id":"https://openalex.org/keywords/flux-limiter","display_name":"Flux limiter","score":0.4973764717578888},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48892489075660706},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41876932978630066},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40009498596191406},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1590687334537506}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.9126816987991333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8550633192062378},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6691397428512573},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6185640096664429},{"id":"https://openalex.org/C2781300812","wikidata":"https://www.wikidata.org/wiki/Q178061","display_name":"Shock (circulatory)","level":2,"score":0.5242859721183777},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5191358923912048},{"id":"https://openalex.org/C10819784","wikidata":"https://www.wikidata.org/wiki/Q5463027","display_name":"Flux limiter","level":2,"score":0.4973764717578888},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48892489075660706},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41876932978630066},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40009498596191406},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1590687334537506},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-00-01254-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01254-0","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01254-0/S0025-5718-00-01254-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.101.1040","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.101.1040","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2001-70-235/S0025-5718-00-01254-0/S0025-5718-00-01254-0.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.4947","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.4947","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2001-70-235/S0025-5718-00-01254-0/S0025-5718-00-01254-0.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01254-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01254-0","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01254-0/S0025-5718-00-01254-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.6499999761581421}],"awards":[{"id":"https://openalex.org/G4130340633","display_name":"Mathematical Sciences:Postdoctoral Research Fellowship","funder_award_id":"9306064","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/F4320309070","display_name":"Brown University","ror":"https://ror.org/05gq02987"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2008358701.pdf","grobid_xml":"https://content.openalex.org/works/W2008358701.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1556248905","https://openalex.org/W1965421536","https://openalex.org/W2008024076","https://openalex.org/W2008077484","https://openalex.org/W2028319149","https://openalex.org/W2043358921","https://openalex.org/W2064534769"],"related_works":["https://openalex.org/W1672500991","https://openalex.org/W2091196763","https://openalex.org/W2041609367","https://openalex.org/W2094862772","https://openalex.org/W4388397561","https://openalex.org/W4382766439","https://openalex.org/W4287661942","https://openalex.org/W2595463258","https://openalex.org/W2380080472","https://openalex.org/W2951370668"],"abstract_inverted_index":{"When":[0],"shock":[1,60,129,209],"speed":[2],"<inline-formula":[3,16,88,148,217],"content-type=\"math/mathml\">":[4,17,89,149,218],"<mml:math":[5,18,90,150,219],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[6,19,91,151,220],"alttext=\"s\">":[7],"<mml:semantics>":[8,29,100,156,231],"<mml:mi>s</mml:mi>":[9,233],"<mml:annotation":[10,46,117,164,249],"encoding=\"application/x-tex\">s</mml:annotation>":[11],"</mml:semantics>":[12,50,120,166,253],"</mml:math>":[13,51,121,167,254],"</inline-formula>":[14,52,122,168,255],"times":[15],"alttext=\"normal":[20],"upper":[21,26,223,228],"Delta":[22,27,224,229],"t":[23,225],"slash":[24,226],"normal":[25,93,98,222,227],"x\">":[28,230],"<mml:mrow>":[30,101,232],"<mml:mi":[31,40,105,112,234,243],"mathvariant=\"normal\">":[32,41,106,113,235,244],"\u0394":[33,42,236,245],"</mml:mi>":[34,43,108,115,237,246],"<mml:mi>t</mml:mi>":[35,238],"<mml:mrow":[36,159,239],"class=\"MJX-TeXAtom-ORD\">":[37,160,240],"<mml:mo>/</mml:mo>":[38,241],"</mml:mrow>":[39,45,116,162,242,248],"<mml:mi>x</mml:mi>":[44,247],"encoding=\"application/x-tex\">\\Delta":[47],"t/\\Delta":[48,251],"x</mml:annotation>":[49,252],"is":[53,74,134,214,256],"rational,":[54],"the":[55,81,125,172,180,191,205],"existence":[56,126,206],"of":[57,59,127,131,138,207],"solutions":[58,83],"profile":[61],"equations":[62],"on":[63],"bounded":[64],"intervals":[65],"for":[66,194,211],"monotonicity":[67,139,144],"preserving":[68,140,145],"schemes":[69,146,213],"with":[70,147,187],"continuous":[71],"numerical":[72,132,169],"flux":[73,170,176,183],"proved.":[75],"A":[76,136],"sufficient":[77],"condition":[78],"under":[79],"which":[80],"above":[82],"can":[84],"be":[85],"extended":[86],"to":[87,200],"alttext=\"negative":[92],"infinity":[94],"greater-than":[95,97],"j":[96],"infinity\">":[99],"<mml:mo>":[102],"\u2212":[103],"</mml:mo>":[104],"\u221e":[107,114],"<mml:mo>&gt;</mml:mo>":[109,111],"<mml:mi>j</mml:mi>":[110],"encoding=\"application/x-tex\">-\\infty":[118],"&gt;j&gt;\\infty</mml:annotation>":[119],",":[123],"implying":[124],"discrete":[128,208],"profiles":[130,210],"schemes,":[133,141],"provided.":[135],"class":[137],"including":[142],"all":[143],"alttext=\"upper":[152],"C":[153],"Superscript":[154],"1\">":[155],"<mml:msup>":[157],"<mml:mi>C</mml:mi>":[158],"<mml:mn>1</mml:mn>":[161],"</mml:msup>":[163],"encoding=\"application/x-tex\">C^{1}</mml:annotation>":[165],"functions,":[171],"second":[173,181],"order":[174,182],"upwinding":[175],"based":[177,184],"MUSCL":[178,185],"scheme,":[179],"scheme":[186,193],"Lax-Friedrichs\u2019":[188],"splitting,":[189],"and":[190],"Godunov":[192],"scalar":[195],"conservation":[196],"laws":[197],"are":[198],"found":[199],"satisfy":[201],"this":[202],"condition.":[203],"Thus,":[204],"these":[212],"established":[215],"when":[216],"alttext=\"s":[221],"encoding=\"application/x-tex\">s\\Delta":[250],"rational.":[257]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
