{"id":"https://openalex.org/W2103650180","doi":"https://doi.org/10.1137/070687840","title":"Traveling Waves and Shocks in a Viscoelastic Generalization of Burgers' Equation","display_name":"Traveling Waves and Shocks in a Viscoelastic Generalization of Burgers' Equation","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2103650180","doi":"https://doi.org/10.1137/070687840","mag":"2103650180"},"language":"en","primary_location":{"id":"doi:10.1137/070687840","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070687840","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/A5027316630","display_name":"Victor Camacho","orcid":null},"institutions":[{"id":"https://openalex.org/I872248612","display_name":"Claremont Colleges","ror":"https://ror.org/03xaz7s88","country_code":"US","type":"education","lineage":["https://openalex.org/I872248612"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Victor Camacho","raw_affiliation_strings":["Claremont Colleges***"],"affiliations":[{"raw_affiliation_string":"Claremont Colleges***","institution_ids":["https://openalex.org/I872248612"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036083892","display_name":"Robert D. Guy","orcid":"https://orcid.org/0000-0002-0602-7015"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert D. Guy","raw_affiliation_strings":["Mathematics Department, University of California Davis, Davis, CA 95616"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of California Davis, Davis, CA 95616","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015813554","display_name":"Jon Jacobsen","orcid":null},"institutions":[{"id":"https://openalex.org/I133543626","display_name":"Harvey Mudd College","ror":"https://ror.org/025ecfn45","country_code":"US","type":"education","lineage":["https://openalex.org/I133543626"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jon Jacobsen","raw_affiliation_strings":["Mathematics Department, Harvey Mudd College, 301 Platt Blvd., Claremont, CA 91711"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Harvey Mudd College, 301 Platt Blvd., Claremont, CA 91711","institution_ids":["https://openalex.org/I133543626"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5027316630"],"corresponding_institution_ids":["https://openalex.org/I872248612"],"apc_list":null,"apc_paid":null,"fwci":0.382,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.67397202,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"68","issue":"5","first_page":"1316","last_page":"1332"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9965000152587891,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9965000152587891,"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/T10524","display_name":"Traffic control and management","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9670000076293945,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7989317178726196},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.7515314817428589},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.696546196937561},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.6624673008918762},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6471272706985474},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6230517029762268},{"id":"https://openalex.org/keywords/viscoelasticity","display_name":"Viscoelasticity","score":0.6090128421783447},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5979000329971313},{"id":"https://openalex.org/keywords/shock-wave","display_name":"Shock wave","score":0.5691205859184265},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.5498575568199158},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.4633021950721741},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3317452669143677},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2907125949859619},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.24946367740631104},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.20904627442359924},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07313597202301025},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.056510865688323975}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7989317178726196},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.7515314817428589},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.696546196937561},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.6624673008918762},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6471272706985474},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6230517029762268},{"id":"https://openalex.org/C186541917","wikidata":"https://www.wikidata.org/wiki/Q910483","display_name":"Viscoelasticity","level":2,"score":0.6090128421783447},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5979000329971313},{"id":"https://openalex.org/C70477161","wikidata":"https://www.wikidata.org/wiki/Q190688","display_name":"Shock wave","level":2,"score":0.5691205859184265},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.5498575568199158},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.4633021950721741},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3317452669143677},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2907125949859619},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.24946367740631104},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.20904627442359924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07313597202301025},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.056510865688323975},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/070687840","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070687840","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:scholarship.claremont.edu:hmc_fac_pub-1769","is_oa":false,"landing_page_url":"https://scholarship.claremont.edu/hmc_fac_pub/764","pdf_url":null,"source":{"id":"https://openalex.org/S4377196412","display_name":"Scholarship - Claremont (Claremont Colleges)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I872248612","host_organization_name":"Claremont Colleges","host_organization_lineage":["https://openalex.org/I872248612"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"All HMC Faculty Publications and Research","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.210.9546","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.210.9546","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ucdavis.edu/%7Eguy/papers/camacho_guy_jacobsen_SIAP.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3134480354","display_name":"Focused Research Groups (FRG): The Dynamics of Growing Biogels","funder_award_id":"0139926","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3228745949","display_name":"Formation and Function of Physiological Gels","funder_award_id":"0540779","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/F4320309332","display_name":"Harvey Mudd College","ror":"https://ror.org/025ecfn45"},{"id":"https://openalex.org/F4320313299","display_name":"Baker Foundation","ror":"https://ror.org/03r1hk592"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W656787405","https://openalex.org/W811954167","https://openalex.org/W1057021034","https://openalex.org/W1494448257","https://openalex.org/W1518050517","https://openalex.org/W1555627060","https://openalex.org/W1580700045","https://openalex.org/W1594751264","https://openalex.org/W1598941160","https://openalex.org/W1602259421","https://openalex.org/W1965134668","https://openalex.org/W1986788497","https://openalex.org/W1999526755","https://openalex.org/W2016660803","https://openalex.org/W2018237065","https://openalex.org/W2034976587","https://openalex.org/W2041001367","https://openalex.org/W2093921901","https://openalex.org/W2095797625","https://openalex.org/W2108433712","https://openalex.org/W2150072667","https://openalex.org/W2152196656","https://openalex.org/W3021722416"],"related_works":["https://openalex.org/W4221057967","https://openalex.org/W4243019676","https://openalex.org/W2517352629","https://openalex.org/W2783562378","https://openalex.org/W4293192718","https://openalex.org/W2045876794","https://openalex.org/W2085019750","https://openalex.org/W2372531153","https://openalex.org/W2347316940","https://openalex.org/W2171321613"],"abstract_inverted_index":{"We":[0],"consider":[1],"traveling":[2,26],"wave":[3],"phenomena":[4],"for":[5,41],"a":[6,42],"viscoelastic":[7],"generalization":[8],"of":[9,21,45,55],"Burgers'":[10],"equation.":[11],"For":[12],"asymptotically":[13],"constant":[14,33],"velocity":[15],"profiles":[16],"we":[17,49],"find":[18],"three":[19],"classes":[20],"solutions":[22],"corresponding":[23],"to":[24],"smooth":[25,29],"waves,":[27,30],"piecewise":[28,32],"and":[31,48,59],"(shock)":[34],"solutions.":[35],"Each":[36],"solution":[37],"type":[38],"is":[39],"possible":[40],"given":[43],"pair":[44],"asymptotic":[46],"limits,":[47],"characterize":[50],"the":[51,56],"dynamics":[52],"in":[53],"terms":[54],"relaxation":[57],"time":[58],"viscosity.":[60]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
