{"id":"https://openalex.org/W2037008679","doi":"https://doi.org/10.1090/s0025-5718-05-01787-4","title":"A semi-implicit monotone difference scheme for an initial-boundary value problem of a strongly degenerate parabolic equation modeling sedimentation-consolidation processes","display_name":"A semi-implicit monotone difference scheme for an initial-boundary value problem of a strongly degenerate parabolic equation modeling sedimentation-consolidation processes","publication_year":2005,"publication_date":"2005-10-21","ids":{"openalex":"https://openalex.org/W2037008679","doi":"https://doi.org/10.1090/s0025-5718-05-01787-4","mag":"2037008679"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-05-01787-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01787-4","pdf_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01787-4/S0025-5718-05-01787-4.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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":"hybrid","oa_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01787-4/S0025-5718-05-01787-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024575553","display_name":"Raimund B\u00fcrger","orcid":"https://orcid.org/0000-0001-9298-8981"},"institutions":[{"id":"https://openalex.org/I172787465","display_name":"University of Concepci\u00f3n","ror":"https://ror.org/0460jpj73","country_code":"CL","type":"education","lineage":["https://openalex.org/I172787465"]}],"countries":["CL"],"is_corresponding":true,"raw_author_name":"Raimund B\u00fcrger","raw_affiliation_strings":["Departamento de Ingenier\u00eda Matem\u00e1tica, Universidad de Concepci\u00f3n, Casilla 160-C, Concepci\u00f3n - Chile"],"affiliations":[{"raw_affiliation_string":"Departamento de Ingenier\u00eda Matem\u00e1tica, Universidad de Concepci\u00f3n, Casilla 160-C, Concepci\u00f3n - Chile","institution_ids":["https://openalex.org/I172787465"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049679352","display_name":"An\u00edbal Coronel","orcid":"https://orcid.org/0000-0001-6602-7378"},"institutions":[{"id":"https://openalex.org/I221450849","display_name":"University of B\u00edo-B\u00edo","ror":"https://ror.org/04dndfk38","country_code":"CL","type":"education","lineage":["https://openalex.org/I221450849"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"An\u00edbal Coronel","raw_affiliation_strings":["Departamento de Ciencias B\u00c3\u00a1sicas, Facultad de Ciencias, Universidad del B\u00c3\u00ado-B\u00c3\u00ado, Casilla 447, Campus Fernando May, Chill\u00c3\u00a1n, Chile","Departamento de Ciencias B\u00e1sicas, Facultad de Ciencias, Universidad del B\u00edo-B\u00edo, Casilla 447, Campus Fernando May, Chill\u00e1n, Chile"],"affiliations":[{"raw_affiliation_string":"Departamento de Ciencias B\u00c3\u00a1sicas, Facultad de Ciencias, Universidad del B\u00c3\u00ado-B\u00c3\u00ado, Casilla 447, Campus Fernando May, Chill\u00c3\u00a1n, Chile","institution_ids":[]},{"raw_affiliation_string":"Departamento de Ciencias B\u00e1sicas, Facultad de Ciencias, Universidad del B\u00edo-B\u00edo, Casilla 447, Campus Fernando May, Chill\u00e1n, Chile","institution_ids":["https://openalex.org/I221450849"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080909641","display_name":"Maur\u00edcio Sep\u00falveda","orcid":"https://orcid.org/0000-0001-8463-3830"},"institutions":[{"id":"https://openalex.org/I172787465","display_name":"University of Concepci\u00f3n","ror":"https://ror.org/0460jpj73","country_code":"CL","type":"education","lineage":["https://openalex.org/I172787465"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Mauricio Sep\u00falveda","raw_affiliation_strings":["Departamento de Ingenier\u00eda Matem\u00e1tica, Universidad de Concepci\u00f3n, Casilla 160-C, Concepci\u00f3n - Chile"],"affiliations":[{"raw_affiliation_string":"Departamento de Ingenier\u00eda Matem\u00e1tica, Universidad de Concepci\u00f3n, Casilla 160-C, Concepci\u00f3n - Chile","institution_ids":["https://openalex.org/I172787465"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5024575553"],"corresponding_institution_ids":["https://openalex.org/I172787465"],"apc_list":null,"apc_paid":null,"fwci":3.4489,"has_fulltext":true,"cited_by_count":25,"citation_normalized_percentile":{"value":0.92775665,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"75","issue":"253","first_page":"91","last_page":"112"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9955000281333923,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9951000213623047,"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/monotone-polygon","display_name":"Monotone polygon","score":0.6052064895629883},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.603947103023529},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5087466835975647},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3670719563961029},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20410054922103882}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6052064895629883},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.603947103023529},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5087466835975647},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3670719563961029},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20410054922103882}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1090/s0025-5718-05-01787-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01787-4","pdf_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01787-4/S0025-5718-05-01787-4.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.3152","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.3152","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/2006-75-253/S0025-5718-05-01787-4/S0025-5718-05-01787-4.pdf","raw_type":"text"},{"id":"pmh:oai:americanae.aecid.es:3267242","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3267242","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MATHEMATICS OF COMPUTATION","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:americanae.aecid.es:3267243","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3267243","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MATHEMATICS OF COMPUTATION","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/176882","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/176882","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MATHEMATICS OF COMPUTATION","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/176883","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/176883","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MATHEMATICS OF COMPUTATION","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-05-01787-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01787-4","pdf_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01787-4/S0025-5718-05-01787-4.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F4320325850","display_name":"Universit\u00e4t Stuttgart","ror":"https://ror.org/04vnq7t77"},{"id":"https://openalex.org/F4320334812","display_name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","ror":"https://ror.org/02ap3w078"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2037008679.pdf","grobid_xml":"https://content.openalex.org/works/W2037008679.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W328073187","https://openalex.org/W1494329389","https://openalex.org/W1549748890","https://openalex.org/W1555674425","https://openalex.org/W1568522471","https://openalex.org/W1593038947","https://openalex.org/W1977839485","https://openalex.org/W1992812527","https://openalex.org/W2028676211","https://openalex.org/W2034939914","https://openalex.org/W2036181736","https://openalex.org/W2036586276","https://openalex.org/W2045679525","https://openalex.org/W2049266244","https://openalex.org/W2057323726","https://openalex.org/W2061030918","https://openalex.org/W2066501150","https://openalex.org/W2067973271","https://openalex.org/W2077744229","https://openalex.org/W2088820595","https://openalex.org/W2107588255","https://openalex.org/W2114463167","https://openalex.org/W2130212979","https://openalex.org/W2134164763","https://openalex.org/W2139038267","https://openalex.org/W2144220295","https://openalex.org/W2147308762","https://openalex.org/W2150347258","https://openalex.org/W2154885094","https://openalex.org/W2326057307","https://openalex.org/W2472436849","https://openalex.org/W2990034374","https://openalex.org/W4205438089","https://openalex.org/W4245010634","https://openalex.org/W4256242560","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"We":[0,45],"prove":[1,92],"the":[2,39,42,47,53,56,95,98,121,129],"convergence":[3,93],"of":[4,41,49,52,58,94,120,126,128],"a":[5,17],"semi-implicit":[6],"monotone":[7],"finite":[8],"difference":[9],"scheme":[10,96],"approximating":[11],"an":[12],"initial-boundary":[13],"value":[14],"problem":[15,36],"for":[16],"spatially":[18],"one-dimensional":[19],"quasilinear":[20],"strongly":[21],"degenerate":[22],"parabolic":[23],"equation,":[24],"which":[25],"is":[26],"supplied":[27],"with":[28],"two":[29],"different":[30],"inhomogeneous":[31],"flux-type":[32],"boundary":[33,130],"conditions.":[34,131],"This":[35],"arises":[37],"in":[38,55],"modeling":[40],"sedimentation-consolidation":[43],"process.":[44],"formulate":[46],"definition":[48],"entropy":[50,118],"solution":[51,119],"model":[54],"sense":[57],"Kru":[59],"<inline-formula":[60,100],"content-type=\"math/mathml\">":[61,101],"<mml:math":[62,102],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[63,103],"alttext=\"ModifyingAbove":[64],"z":[65],"With":[66],"\u02c7\">":[67],"<mml:semantics>":[68,108],"<mml:mrow":[69],"class=\"MJX-TeXAtom-ORD\">":[70],"<mml:mover>":[71],"<mml:mstyle":[72],"displaystyle=\"false\"":[73],"scriptlevel=\"0\">":[74],"<mml:mtext>z</mml:mtext>":[75],"</mml:mstyle>":[76],"<mml:mo":[77],"stretchy=\"false\">":[78],"\u02c7":[79],"</mml:mo>":[80],"</mml:mover>":[81],"</mml:mrow>":[82,112],"<mml:annotation":[83,113],"encoding=\"application/x-tex\">\\check":[84],"{\\mbox":[85],"{z}}</mml:annotation>":[86],"</mml:semantics>":[87,115],"</mml:math>":[88,116],"</inline-formula>":[89,117],"kov":[90],"and":[91],"to":[97,124],"unique":[99],"alttext=\"upper":[104],"B":[105],"upper":[106],"V\">":[107],"<mml:mrow>":[109],"<mml:mi>B</mml:mi>":[110],"<mml:mi>V</mml:mi>":[111],"encoding=\"application/x-tex\">BV</mml:annotation>":[114],"problem,":[122],"up":[123],"satisfaction":[125],"one":[127]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}