{"id":"https://openalex.org/W4415095990","doi":"https://doi.org/10.3934/nhm.2025046","title":"A non-conservative, non-local approximation of the Burgers equation","display_name":"A non-conservative, non-local approximation of the Burgers equation","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4415095990","doi":"https://doi.org/10.3934/nhm.2025046"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2025046","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2025046","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/nhm.2025046","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035084695","display_name":"Shyam Sundar Ghoshal","orcid":"https://orcid.org/0000-0002-6242-2327"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shyam Sundar Ghoshal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Parasuram Venkatesh","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Parasuram Venkatesh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003850935","display_name":"Emil Wiedemann","orcid":"https://orcid.org/0000-0002-1401-3078"},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]},{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE","IN"],"is_corresponding":false,"raw_author_name":"Emil Wiedemann","raw_affiliation_strings":["Centre for Applicable Mathematics, Tata Institute of Fundamental Research, India","Department of Mathematics, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Applicable Mathematics, Tata Institute of Fundamental Research, India","institution_ids":["https://openalex.org/I11947397"]},{"raw_affiliation_string":"Department of Mathematics, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Germany","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035084695"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.38168159,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"4","first_page":"1061","last_page":"1086"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9976999759674072,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9976999759674072,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9959999918937683,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9958999752998352,"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/burgers-equation","display_name":"Burgers' equation","score":0.7024999856948853},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.6606000065803528},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6535000205039978},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.505299985408783},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4991999864578247},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4968999922275543},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.4797999858856201},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.4681999981403351},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4569999873638153}],"concepts":[{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.7024999856948853},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.6606000065803528},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6535000205039978},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6391000151634216},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5547999739646912},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.505299985408783},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49970000982284546},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4991999864578247},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4968999922275543},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.4797999858856201},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4681999981403351},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4569999873638153},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4108000099658966},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.40619999170303345},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.40149998664855957},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.34279999136924744},{"id":"https://openalex.org/C2780719617","wikidata":"https://www.wikidata.org/wiki/Q1030752","display_name":"Salient","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.3411000072956085},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.3400999903678894},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.3395000100135803},{"id":"https://openalex.org/C2775918384","wikidata":"https://www.wikidata.org/wiki/Q4660961","display_name":"A priori estimate","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C146324458","wikidata":"https://www.wikidata.org/wiki/Q1202673","display_name":"Uniform norm","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C135909967","wikidata":"https://www.wikidata.org/wiki/Q4338245","display_name":"Singular solution","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2025046","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2025046","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ee0a2d9c2dd1429ca895cf2bf762f9af","is_oa":false,"landing_page_url":"https://doaj.org/article/ee0a2d9c2dd1429ca895cf2bf762f9af","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 20, Iss 4, Pp 1061-1086 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2025046","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2025046","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1555627060","https://openalex.org/W1992812527","https://openalex.org/W2009713111","https://openalex.org/W2034766833","https://openalex.org/W2035184790","https://openalex.org/W2073078790","https://openalex.org/W2132835045","https://openalex.org/W2171722718","https://openalex.org/W2395691577","https://openalex.org/W2529192566","https://openalex.org/W2566163163","https://openalex.org/W2618274270","https://openalex.org/W2798744386","https://openalex.org/W2894642221","https://openalex.org/W2924883007","https://openalex.org/W2963110170","https://openalex.org/W2963600615","https://openalex.org/W3101267478","https://openalex.org/W3103172194","https://openalex.org/W3115175543","https://openalex.org/W3117315487","https://openalex.org/W3170829831","https://openalex.org/W3171181309","https://openalex.org/W4205236375","https://openalex.org/W4283273950","https://openalex.org/W4307648536","https://openalex.org/W4391358059","https://openalex.org/W4393049991","https://openalex.org/W4396677623","https://openalex.org/W4409974726"],"related_works":[],"abstract_inverted_index":{"The":[0,41],"analysis":[1],"of":[2,5,15,44,79,129,137],"non-local":[3,35],"regularisations":[4,128],"scalar":[6],"conservation":[7,83],"laws":[8],"is":[9,47],"an":[10,33],"active":[11],"research":[12],"program.":[13],"Applications":[14],"such":[16,24,108],"equations":[17],"are":[18],"found":[19],"in":[20,37],"modelling":[21],"physical":[22],"phenomena,":[23],"as":[25,109],"traffic":[26],"flow.":[27],"In":[28],"this":[29,85],"paper,":[30],"we":[31,49,90,114,123],"propose":[32],"inviscid,":[34],"regularisation":[36],"a":[38,53],"non-divergence":[39],"form.":[40],"salient":[42],"feature":[43],"our":[45],"approach":[46],"that":[48],"can":[50],"obtain":[51],"sharp":[52],"priori":[54],"estimates":[55],"on":[56,118],"the":[57,68,77,95,103,111,119,130,134,140],"total":[58],"variation":[59],"$":[60,62],"(TV)":[61],"and":[63,66],"supremum":[64],"norm":[65],"justify":[67],"singular":[69,120],"limit":[70],"for":[71,110],"Lipschitz":[72],"initial":[73,96,145],"data":[74,97],"up":[75],"to":[76,127,139],"time":[78],"catastrophe.":[80],"For":[81],"generic":[82],"laws,":[84],"result":[86],"was":[87,106],"sharp,":[88],"since":[89],"could":[91],"demonstrate":[92],"non-convergence":[93],"when":[94,102],"featured":[98],"simple":[99],"discontinuities.":[100],"However,":[101],"flux":[104],"derivative":[105],"linear,":[107],"Burgers":[112,131],"equation,":[113,132],"obtained":[115],"stronger":[116],"limits":[117],"limit.":[121],"Therefore,":[122],"devoted":[124],"special":[125],"attention":[126],"specifically":[133],"limiting":[135],"behaviour":[136],"solutions":[138],"Cauchy":[141],"problems":[142],"with":[143],"fixed":[144],"data.":[146]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-13T00:00:00"}