{"id":"https://openalex.org/W2049938098","doi":"https://doi.org/10.1090/s0025-5718-96-00733-8","title":"Nonlinear stability of stationary discrete shocks for nonconvex scalar conservation laws","display_name":"Nonlinear stability of stationary discrete shocks for nonconvex scalar conservation laws","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2049938098","doi":"https://doi.org/10.1090/s0025-5718-96-00733-8","mag":"2049938098"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-96-00733-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00733-8","pdf_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00733-8/S0025-5718-96-00733-8.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/1996-65-215/S0025-5718-96-00733-8/S0025-5718-96-00733-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009678665","display_name":"Hailiang Liu","orcid":"https://orcid.org/0000-0003-1643-931X"},"institutions":[{"id":"https://openalex.org/I75955062","display_name":"Henan Normal University","ror":"https://ror.org/00s13br28","country_code":"CN","type":"education","lineage":["https://openalex.org/I75955062"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hailiang Liu","raw_affiliation_strings":["Department of Mathematics, Henan Normal University, Xinxiang 453002, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Henan Normal University, Xinxiang 453002, P. R. China","institution_ids":["https://openalex.org/I75955062"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067255425","display_name":"Jinghua Wang","orcid":"https://orcid.org/0000-0001-9457-6059"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinghua Wang","raw_affiliation_strings":["Institute of Systems Science, Academia Sinica, Beijing 100080, P.R.China"],"affiliations":[{"raw_affiliation_string":"Institute of Systems Science, Academia Sinica, Beijing 100080, P.R.China","institution_ids":["https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009678665"],"corresponding_institution_ids":["https://openalex.org/I75955062"],"apc_list":null,"apc_paid":null,"fwci":2.0042,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.84989254,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"215","first_page":"1137","last_page":"1153"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9991999864578247,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.9991999864578247,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9912999868392944,"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/conservation-law","display_name":"Conservation law","score":0.6505585312843323},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.6178740859031677},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.57317054271698},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5137730836868286},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4986131191253662},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49237334728240967},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4107692241668701},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26348668336868286},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22132918238639832},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13125941157341003},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.08743825554847717},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07846862077713013},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07274860143661499}],"concepts":[{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.6505585312843323},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6178740859031677},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.57317054271698},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5137730836868286},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4986131191253662},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49237334728240967},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4107692241668701},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26348668336868286},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22132918238639832},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13125941157341003},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.08743825554847717},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07846862077713013},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07274860143661499}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-96-00733-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00733-8","pdf_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00733-8/S0025-5718-96-00733-8.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:10.1.1.96.8252","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.96.8252","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/1996-65-215/S0025-5718-96-00733-8/S0025-5718-96-00733-8.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-96-00733-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00733-8","pdf_url":"https://www.ams.org/mcom/1996-65-215/S0025-5718-96-00733-8/S0025-5718-96-00733-8.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":[{"score":0.6299999952316284,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321041","display_name":"Academia Sinica","ror":"https://ror.org/05bxb3784"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2049938098.pdf","grobid_xml":"https://content.openalex.org/works/W2049938098.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W1550599649","https://openalex.org/W1568522471","https://openalex.org/W1998494429","https://openalex.org/W2000769938","https://openalex.org/W2008076987","https://openalex.org/W2009395216","https://openalex.org/W2020168202","https://openalex.org/W2024626215","https://openalex.org/W2027087330","https://openalex.org/W2028981787","https://openalex.org/W2043358921","https://openalex.org/W2044884780","https://openalex.org/W2045679525","https://openalex.org/W2058221859","https://openalex.org/W2064534769","https://openalex.org/W2070344813","https://openalex.org/W2089187699","https://openalex.org/W2095375160","https://openalex.org/W2098661141","https://openalex.org/W2112543799","https://openalex.org/W2335584542","https://openalex.org/W2499202822","https://openalex.org/W2573847088","https://openalex.org/W2783879869","https://openalex.org/W3216299223","https://openalex.org/W4214820058","https://openalex.org/W4232154088","https://openalex.org/W4232833152","https://openalex.org/W4235839826","https://openalex.org/W4237364439","https://openalex.org/W4241293999","https://openalex.org/W4285719527"],"related_works":["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/W2765737651","https://openalex.org/W2181555576","https://openalex.org/W2476202684","https://openalex.org/W2296698021"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,34,66],"to":[3,30,76],"study":[4],"the":[5,13,23,26,44,47],"asymptotic":[6],"stability":[7,65],"of":[8,25,72],"stationary":[9],"discrete":[10],"shocks":[11],"for":[12],"Lax-Friedrichs":[14],"scheme":[15],"approximating":[16],"nonconvex":[17],"scalar":[18],"conservation":[19],"laws,":[20],"provided":[21],"that":[22],"summations":[24],"initial":[27],"perturbations":[28],"equal":[29],"zero.":[31],"The":[32,69],"result":[33],"proved":[35],"by":[36],"using":[37],"a":[38,78],"weighted":[39],"energy":[40],"method":[41],"based":[42],"on":[43],"nonconvexity.":[45],"Moreover,":[46],"<inline-formula":[48],"content-type=\"math/mathml\">":[49],"<mml:math":[50],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[51],"alttext=\"l":[52],"Superscript":[53],"1\">":[54],"<mml:semantics>":[55],"<mml:msup>":[56],"<mml:mi>l</mml:mi>":[57],"<mml:mn>1</mml:mn>":[58],"</mml:msup>":[59],"<mml:annotation":[60],"encoding=\"application/x-tex\">l^1</mml:annotation>":[61],"</mml:semantics>":[62],"</mml:math>":[63],"</inline-formula>":[64],"also":[67],"obtained.":[68],"key":[70],"points":[71],"our":[73],"proofs":[74],"are":[75],"choose":[77],"suitable":[79],"weight":[80],"function.":[81]},"counts_by_year":[],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}