Backward Uniqueness for Parabolic Equations View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2003-09

AUTHORS

L. Escauriaza, G. Seregin, V. Šverák

ABSTRACT

It is shown that a function u satisfying |∂t+Δu|≦M(|u|+|∇u|), |u(x, t)|≦MeM|x|2 in (ℝn \ (BR) × [0, T] and u(x, 0) = 0 for xℝn \ BR must vanish identically in ℝn \ BR×[0, T].

PAGES

147-157

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00205-003-0263-8

DOI

http://dx.doi.org/10.1007/s00205-003-0263-8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1052817011


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

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", 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of the Basque Country", 
          "id": "https://www.grid.ac/institutes/grid.11480.3c", 
          "name": [
            "Dpto. de Matem\u00e1ticas, UPV/EHU, 48080, Bilbao, Spain"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Escauriaza", 
        "givenName": "L.", 
        "id": "sg:person.011107432025.24", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011107432025.24"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Steklov Mathematical Institute", 
          "id": "https://www.grid.ac/institutes/grid.426543.2", 
          "name": [
            "Steklov Institute of Mathematics, St.Peterburg, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Seregin", 
        "givenName": "G.", 
        "id": "sg:person.016605632647.12", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016605632647.12"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Minnesota", 
          "id": "https://www.grid.ac/institutes/grid.17635.36", 
          "name": [
            "School of Mathematics, University of Minnesota, Minneapolis, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "\u0160ver\u00e1k", 
        "givenName": "V.", 
        "id": "sg:person.01154016310.87", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01154016310.87"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf01174182", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005099440", 
          "https://doi.org/10.1007/bf01174182"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01174182", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005099440", 
          "https://doi.org/10.1007/bf01174182"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02384566", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020428461", 
          "https://doi.org/10.1007/bf02384566"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02384566", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1020428461", 
          "https://doi.org/10.1007/bf02384566"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/03605308308820262", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022029638"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0022-0396(87)90043-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022499846"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-46175-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029183879", 
          "https://doi.org/10.1007/978-3-642-46175-0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-46175-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029183879", 
          "https://doi.org/10.1007/978-3-642-46175-0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/03605309608821195", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030453527"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/mana.3210040121", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036595171"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02387373", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041124059", 
          "https://doi.org/10.1007/bf02387373"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02387373", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041124059", 
          "https://doi.org/10.1007/bf02387373"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s002080050202", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050213807", 
          "https://doi.org/10.1007/s002080050202"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0022-247x(77)90021-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052708749"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1215/s0012-7094-00-10415-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064415124"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1512/iumj.2001.50.1937", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1067513233"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4615-0701-7_19", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1089530294", 
          "https://doi.org/10.1007/978-1-4615-0701-7_19"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4615-0701-7_19", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1089530294", 
          "https://doi.org/10.1007/978-1-4615-0701-7_19"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/mmono/023", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1101567800"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2003-09", 
    "datePublishedReg": "2003-09-01", 
    "description": "It is shown that a function u satisfying |\u2202t+\u0394u|\u2266M(|u|+|\u2207u|), |u(x, t)|\u2266MeM|x|2 in (\u211dn \\ (BR) \u00d7 [0, T] and u(x, 0) = 0 for x\ue3a2\u211dn \\ BR must vanish identically in \u211dn \\ BR\u00d7[0, T].", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s00205-003-0263-8", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1047617", 
        "issn": [
          "0003-9527", 
          "1432-0673"
        ], 
        "name": "Archive for Rational Mechanics and Analysis", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "169"
      }
    ], 
    "name": "Backward Uniqueness for Parabolic Equations", 
    "pagination": "147-157", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "fb955a5896f6a7fe10f3720479839e0206d28ff918895a770a6b49c7d9d85c48"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00205-003-0263-8"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1052817011"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00205-003-0263-8", 
      "https://app.dimensions.ai/details/publication/pub.1052817011"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T14:26", 
    "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/v90/0000000373_0000000373/records_13069_00000002.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs00205-003-0263-8"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

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/s00205-003-0263-8'

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/s00205-003-0263-8'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00205-003-0263-8'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00205-003-0263-8'


 

This table displays all metadata directly associated to this object as RDF triples.

121 TRIPLES      20 PREDICATES      39 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00205-003-0263-8 schema:author N640dfad940ab4274b99e36dce1e911e6
2 schema:citation sg:pub.10.1007/978-1-4615-0701-7_19
3 sg:pub.10.1007/978-3-642-46175-0
4 sg:pub.10.1007/bf01174182
5 sg:pub.10.1007/bf02384566
6 sg:pub.10.1007/bf02387373
7 sg:pub.10.1007/s002080050202
8 https://doi.org/10.1002/mana.3210040121
9 https://doi.org/10.1016/0022-0396(87)90043-x
10 https://doi.org/10.1016/0022-247x(77)90021-x
11 https://doi.org/10.1080/03605308308820262
12 https://doi.org/10.1080/03605309608821195
13 https://doi.org/10.1090/mmono/023
14 https://doi.org/10.1215/s0012-7094-00-10415-2
15 https://doi.org/10.1512/iumj.2001.50.1937
16 schema:datePublished 2003-09
17 schema:datePublishedReg 2003-09-01
18 schema:description It is shown that a function u satisfying |∂t+Δu|≦M(|u|+|∇u|), |u(x, t)|≦MeM|x|2 in (ℝn \ (BR) × [0, T] and u(x, 0) = 0 for xℝn \ BR must vanish identically in ℝn \ BR×[0, T].
19 schema:genre research_article
20 schema:inLanguage en
21 schema:isAccessibleForFree true
22 schema:isPartOf N9924a1c0c3a04e27a8d8768c12abc825
23 Nbe1a5442ec3b4697b9271420fefecbef
24 sg:journal.1047617
25 schema:name Backward Uniqueness for Parabolic Equations
26 schema:pagination 147-157
27 schema:productId N616790f96a544cedbe7c8d1a4a3124a0
28 N6302a629383942eaa48dffe8a852ebda
29 N93be4422427a47f29bc2f3f330e5bcba
30 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052817011
31 https://doi.org/10.1007/s00205-003-0263-8
32 schema:sdDatePublished 2019-04-11T14:26
33 schema:sdLicense https://scigraph.springernature.com/explorer/license/
34 schema:sdPublisher Nb88069ab93a64e69b0ad9c40471aae06
35 schema:url http://link.springer.com/10.1007%2Fs00205-003-0263-8
36 sgo:license sg:explorer/license/
37 sgo:sdDataset articles
38 rdf:type schema:ScholarlyArticle
39 N5cfb9644569b4bda9f99c6b9c93a9a4e rdf:first sg:person.01154016310.87
40 rdf:rest rdf:nil
41 N616790f96a544cedbe7c8d1a4a3124a0 schema:name doi
42 schema:value 10.1007/s00205-003-0263-8
43 rdf:type schema:PropertyValue
44 N6302a629383942eaa48dffe8a852ebda schema:name readcube_id
45 schema:value fb955a5896f6a7fe10f3720479839e0206d28ff918895a770a6b49c7d9d85c48
46 rdf:type schema:PropertyValue
47 N640dfad940ab4274b99e36dce1e911e6 rdf:first sg:person.011107432025.24
48 rdf:rest N9706356175444025880f66bfb5aea2c5
49 N93be4422427a47f29bc2f3f330e5bcba schema:name dimensions_id
50 schema:value pub.1052817011
51 rdf:type schema:PropertyValue
52 N9706356175444025880f66bfb5aea2c5 rdf:first sg:person.016605632647.12
53 rdf:rest N5cfb9644569b4bda9f99c6b9c93a9a4e
54 N9924a1c0c3a04e27a8d8768c12abc825 schema:volumeNumber 169
55 rdf:type schema:PublicationVolume
56 Nb88069ab93a64e69b0ad9c40471aae06 schema:name Springer Nature - SN SciGraph project
57 rdf:type schema:Organization
58 Nbe1a5442ec3b4697b9271420fefecbef schema:issueNumber 2
59 rdf:type schema:PublicationIssue
60 sg:journal.1047617 schema:issn 0003-9527
61 1432-0673
62 schema:name Archive for Rational Mechanics and Analysis
63 rdf:type schema:Periodical
64 sg:person.011107432025.24 schema:affiliation https://www.grid.ac/institutes/grid.11480.3c
65 schema:familyName Escauriaza
66 schema:givenName L.
67 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011107432025.24
68 rdf:type schema:Person
69 sg:person.01154016310.87 schema:affiliation https://www.grid.ac/institutes/grid.17635.36
70 schema:familyName Šverák
71 schema:givenName V.
72 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01154016310.87
73 rdf:type schema:Person
74 sg:person.016605632647.12 schema:affiliation https://www.grid.ac/institutes/grid.426543.2
75 schema:familyName Seregin
76 schema:givenName G.
77 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016605632647.12
78 rdf:type schema:Person
79 sg:pub.10.1007/978-1-4615-0701-7_19 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089530294
80 https://doi.org/10.1007/978-1-4615-0701-7_19
81 rdf:type schema:CreativeWork
82 sg:pub.10.1007/978-3-642-46175-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029183879
83 https://doi.org/10.1007/978-3-642-46175-0
84 rdf:type schema:CreativeWork
85 sg:pub.10.1007/bf01174182 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005099440
86 https://doi.org/10.1007/bf01174182
87 rdf:type schema:CreativeWork
88 sg:pub.10.1007/bf02384566 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020428461
89 https://doi.org/10.1007/bf02384566
90 rdf:type schema:CreativeWork
91 sg:pub.10.1007/bf02387373 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041124059
92 https://doi.org/10.1007/bf02387373
93 rdf:type schema:CreativeWork
94 sg:pub.10.1007/s002080050202 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050213807
95 https://doi.org/10.1007/s002080050202
96 rdf:type schema:CreativeWork
97 https://doi.org/10.1002/mana.3210040121 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036595171
98 rdf:type schema:CreativeWork
99 https://doi.org/10.1016/0022-0396(87)90043-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1022499846
100 rdf:type schema:CreativeWork
101 https://doi.org/10.1016/0022-247x(77)90021-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1052708749
102 rdf:type schema:CreativeWork
103 https://doi.org/10.1080/03605308308820262 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022029638
104 rdf:type schema:CreativeWork
105 https://doi.org/10.1080/03605309608821195 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030453527
106 rdf:type schema:CreativeWork
107 https://doi.org/10.1090/mmono/023 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101567800
108 rdf:type schema:CreativeWork
109 https://doi.org/10.1215/s0012-7094-00-10415-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064415124
110 rdf:type schema:CreativeWork
111 https://doi.org/10.1512/iumj.2001.50.1937 schema:sameAs https://app.dimensions.ai/details/publication/pub.1067513233
112 rdf:type schema:CreativeWork
113 https://www.grid.ac/institutes/grid.11480.3c schema:alternateName University of the Basque Country
114 schema:name Dpto. de Matemáticas, UPV/EHU, 48080, Bilbao, Spain
115 rdf:type schema:Organization
116 https://www.grid.ac/institutes/grid.17635.36 schema:alternateName University of Minnesota
117 schema:name School of Mathematics, University of Minnesota, Minneapolis, USA
118 rdf:type schema:Organization
119 https://www.grid.ac/institutes/grid.426543.2 schema:alternateName Steklov Mathematical Institute
120 schema:name Steklov Institute of Mathematics, St.Peterburg, Russia
121 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...