Ontology type: schema:Chapter Open Access: True
2013
AUTHORSLuigi Ambrosio , Alberto Bressan , Dirk Helbing , Axel Klar , Enrique Zuazua
ABSTRACTThese notes provide an introduction to the theory of hyperbolic systems of conservation laws in one space dimension. The various chapters cover the following topics: (1) Meaning of a conservation equation and definition of weak solutions. (2) Hyperbolic systems. Explicit solutions in the linear, constant coefficients case. Nonlinear effects: loss of regularity and wave interactions. (3) Shock waves: Rankine–Hugoniot equations and admissibility conditions. (4) Genuinely nonlinear and linearly degenerate characteristic fields. Centered rarefaction waves. The general solution of the Riemann problem. Wave interaction estimates. (5) Weak solutions to the Cauchy problem, with initial data having small total variation. Approximations generated by the front-tracking method and by the Glimm scheme. (6) Continuous dependence of solutions w.r.t. the initial data, in the L 1 distance. (7) Characterization of solutions which are limits of front tracking approximations. Uniqueness of entropy-admissible weak solutions. (8) Vanishing viscosity approximations. (9) Extensions and open problems. The survey is concluded with an Appendix, reviewing some basic analytical tools used in the previous sections.Throughout the exposition, technical details are mostly left out. The main goal of these notes is to convey basic ideas, also with the aid of a large number of figures. More... »
PAGES157-245
Modelling and Optimisation of Flows on Networks
ISBN
978-3-642-32159-7
978-3-642-32160-3
http://scigraph.springernature.com/pub.10.1007/978-3-642-32160-3_2
DOIhttp://dx.doi.org/10.1007/978-3-642-32160-3_2
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1023366595
JSON-LD is the canonical representation for SciGraph data.
TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT
[
{
"@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json",
"about": [
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Pure Mathematics",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Mathematical Sciences",
"type": "DefinedTerm"
}
],
"author": [
{
"familyName": "Ambrosio",
"givenName": "Luigi",
"id": "sg:person.012621721115.68",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012621721115.68"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Pennsylvania State University",
"id": "https://www.grid.ac/institutes/grid.29857.31",
"name": [
"Department of Mathematics, Penn State University, University Park, PA\u00a016802, USA"
],
"type": "Organization"
},
"familyName": "Bressan",
"givenName": "Alberto",
"id": "sg:person.0754214334.90",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0754214334.90"
],
"type": "Person"
},
{
"familyName": "Helbing",
"givenName": "Dirk",
"id": "sg:person.01127352226.45",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01127352226.45"
],
"type": "Person"
},
{
"familyName": "Klar",
"givenName": "Axel",
"id": "sg:person.010553155452.86",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010553155452.86"
],
"type": "Person"
},
{
"familyName": "Zuazua",
"givenName": "Enrique",
"id": "sg:person.016600410137.78",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016600410137.78"
],
"type": "Person"
}
],
"citation": [
{
"id": "https://doi.org/10.1002/cpa.20141",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1000828993"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0022-247x(92)90027-b",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1001970857"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0022-247x(72)90114-x",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1002989770"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0022-0396(75)90091-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1006583330"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00205-007-0052-x",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1008669346",
"https://doi.org/10.1007/s00205-007-0052-x"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00205-007-0052-x",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1008669346",
"https://doi.org/10.1007/s00205-007-0052-x"
],
"type": "CreativeWork"
},
{
"id": "https://app.dimensions.ai/details/publication/pub.1008967360",
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-56139-9",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1008967360",
"https://doi.org/10.1007/978-3-642-56139-9"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-56139-9",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1008967360",
"https://doi.org/10.1007/978-3-642-56139-9"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/cpa.20030",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1009053107"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf00410614",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1009329073",
"https://doi.org/10.1007/bf00410614"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf00410614",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1009329073",
"https://doi.org/10.1007/bf00410614"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s002050050143",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1015059441",
"https://doi.org/10.1007/s002050050143"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/cpa.3160180408",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1015640913"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/cpa.3160180408",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1015640913"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00030-007-5010-7",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1021372124",
"https://doi.org/10.1007/s00030-007-5010-7"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1090/s0894-0347-99-00292-1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1022321320"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00205-009-0248-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1025503177",
"https://doi.org/10.1007/s00205-009-0248-3"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00205-009-0248-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1025503177",
"https://doi.org/10.1007/s00205-009-0248-3"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00205-009-0248-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1025503177",
"https://doi.org/10.1007/s00205-009-0248-3"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s002050050165",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1028655139",
"https://doi.org/10.1007/s002050050165"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf02764657",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1029887850",
"https://doi.org/10.1007/bf02764657"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s002050200198",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1030694835",
"https://doi.org/10.1007/s002050200198"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00205-004-0325-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1031393006",
"https://doi.org/10.1007/s00205-004-0325-6"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00205-004-0325-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1031393006",
"https://doi.org/10.1007/s00205-004-0325-6"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf00375350",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1031570730",
"https://doi.org/10.1007/bf00375350"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf00375350",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1031570730",
"https://doi.org/10.1007/bf00375350"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/j.jde.2005.03.010",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1031679636"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1006/jdeq.1998.3606",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1032190333"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/cpa.3160300605",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1032884696"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/cpa.3160300605",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1032884696"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0022-0396(76)90102-9",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1035720144"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01625772",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1035844892",
"https://doi.org/10.1007/bf01625772"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0022-0396(91)90124-r",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1039763997"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf00251724",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1040419078",
"https://doi.org/10.1007/bf00251724"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf00251724",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1040419078",
"https://doi.org/10.1007/bf00251724"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf00251724",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1040419078",
"https://doi.org/10.1007/bf00251724"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/cpa.3160100406",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1041027283"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1002/cpa.3160100406",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1041027283"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1006/jmaa.1997.5715",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1043873685"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s002050050088",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1044707122",
"https://doi.org/10.1007/s002050050088"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-1-4684-0152-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1045736858",
"https://doi.org/10.1007/978-1-4684-0152-3"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-1-4684-0152-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1045736858",
"https://doi.org/10.1007/978-1-4684-0152-3"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1016/0022-247x(76)90146-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1048312162"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf00392027",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1052089384",
"https://doi.org/10.1007/bf00392027"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf00392027",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1052089384",
"https://doi.org/10.1007/bf00392027"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s002050050068",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1052618085",
"https://doi.org/10.1007/s002050050068"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1070/sm1967v002n02abeh002340",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1058198624"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1137/s0036141002403110",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1062875850"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1137/s0036141099352339",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1062876610"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.1512/iumj.1999.48.1601",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1067513093"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.3934/dcds.2000.6.673",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1071732794"
],
"type": "CreativeWork"
},
{
"id": "https://doi.org/10.4007/annals.2005.161.223",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1071866903"
],
"type": "CreativeWork"
}
],
"datePublished": "2013",
"datePublishedReg": "2013-01-01",
"description": "These notes provide an introduction to the theory of hyperbolic systems of conservation laws in one space dimension. The various chapters cover the following topics: (1) Meaning of a conservation equation and definition of weak solutions. (2) Hyperbolic systems. Explicit solutions in the linear, constant coefficients case. Nonlinear effects: loss of regularity and wave interactions. (3) Shock waves: Rankine\u2013Hugoniot equations and admissibility conditions. (4) Genuinely nonlinear and linearly degenerate characteristic fields. Centered rarefaction waves. The general solution of the Riemann problem. Wave interaction estimates. (5) Weak solutions to the Cauchy problem, with initial data having small total variation. Approximations generated by the front-tracking method and by the Glimm scheme. (6) Continuous dependence of solutions w.r.t. the initial data, in the L 1 distance. (7) Characterization of solutions which are limits of front tracking approximations. Uniqueness of entropy-admissible weak solutions. (8) Vanishing viscosity approximations. (9) Extensions and open problems. The survey is concluded with an Appendix, reviewing some basic analytical tools used in the previous sections.Throughout the exposition, technical details are mostly left out. The main goal of these notes is to convey basic ideas, also with the aid of a large number of figures.",
"genre": "chapter",
"id": "sg:pub.10.1007/978-3-642-32160-3_2",
"inLanguage": [
"en"
],
"isAccessibleForFree": true,
"isPartOf": {
"isbn": [
"978-3-642-32159-7",
"978-3-642-32160-3"
],
"name": "Modelling and Optimisation of Flows on Networks",
"type": "Book"
},
"name": "Hyperbolic Conservation Laws: An Illustrated Tutorial",
"pagination": "157-245",
"productId": [
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/978-3-642-32160-3_2"
]
},
{
"name": "readcube_id",
"type": "PropertyValue",
"value": [
"6f534fa10f2316bd462b8732639b7cf3fbeb319785b0e68ce307f5c86dbd2fe5"
]
},
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1023366595"
]
}
],
"publisher": {
"location": "Berlin, Heidelberg",
"name": "Springer Berlin Heidelberg",
"type": "Organisation"
},
"sameAs": [
"https://doi.org/10.1007/978-3-642-32160-3_2",
"https://app.dimensions.ai/details/publication/pub.1023366595"
],
"sdDataset": "chapters",
"sdDatePublished": "2019-04-15T11:34",
"sdLicense": "https://scigraph.springernature.com/explorer/license/",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8660_00000257.jsonl",
"type": "Chapter",
"url": "http://link.springer.com/10.1007/978-3-642-32160-3_2"
}
]Download the RDF metadata as: json-ld nt turtle xml License info
JSON-LD is a popular format for linked data which is fully compatible with JSON.
curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-32160-3_2'
N-Triples is a line-based linked data format ideal for batch operations.
curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-32160-3_2'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-32160-3_2'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-642-32160-3_2'
This table displays all metadata directly associated to this object as RDF triples.
216 TRIPLES
22 PREDICATES
65 URIs
19 LITERALS
7 BLANK NODES