Indirect internal stabilization of weakly coupled evolution equations View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2002-05

AUTHORS

F. Alabau, P. Cannarsa, V. Komornik

ABSTRACT

Let two second order evolution equations be coupled via the zero order terms, and suppose that the first one is stabilized by a distributed feedback. What will then be the effect of such a partial stabilization on the decay of solutions at infinity? Is the behaviour of the first component sufficient to stabilize the second one? The answer given in this paper is that sufficiently smooth solutions decay polynomially at infinity, and that this decay rate is, in some sense, optimal. The stabilization result for abstract evolution equations is also applied to study the asymptotic behaviour of various systems of partial differential equations. More... »

PAGES

127-150

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00028-002-8083-0

DOI

http://dx.doi.org/10.1007/s00028-002-8083-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1026549559


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", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0102", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Applied 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": [
      {
        "affiliation": {
          "alternateName": "University of Lorraine", 
          "id": "https://www.grid.ac/institutes/grid.29172.3f", 
          "name": [
            "D\u00e9partement de Math\u00e9matique, Universit\u00e9 de Metz, Ile du Saulcy, 57000 Metz, France,, FR"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Alabau", 
        "givenName": "F.", 
        "id": "sg:person.014476532013.27", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014476532013.27"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Rome Tor Vergata", 
          "id": "https://www.grid.ac/institutes/grid.6530.0", 
          "name": [
            "Dipartimento di Matematica, Universit\u00e0 di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Roma, Italy, e-mail: cannarsa@axp.mat.uniroma2.it, IT"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Cannarsa", 
        "givenName": "P.", 
        "id": "sg:person.014257010655.09", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014257010655.09"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Institut de Recherche Math\u00e9matique Avanc\u00e9e", 
          "id": "https://www.grid.ac/institutes/grid.469947.1", 
          "name": [
            "Institut de Recherche Math\u00e9matique Avanc\u00e9e, Universit\u00e9 Louis Pasteur et CNRS, 7, rue Ren\u00e9 Descartes, 67084 Strasbourg Cedex, France, FR"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Komornik", 
        "givenName": "V.", 
        "id": "sg:person.013053062253.94", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013053062253.94"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/0022-0396(75)90009-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006374149"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0764-4442(99)80316-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014128701"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s002330010042", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030090666", 
          "https://doi.org/10.1007/s002330010042"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jmaa.1993.1071", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033914765"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jmaa.1999.6678", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042865492"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/0318022", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062843520"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s0363012997317505", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062881341"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2002-05", 
    "datePublishedReg": "2002-05-01", 
    "description": "Let two second order evolution equations be coupled via the zero order terms, and suppose that the first one is stabilized by a distributed feedback. What will then be the effect of such a partial stabilization on the decay of solutions at infinity? Is the behaviour of the first component sufficient to stabilize the second one? The answer given in this paper is that sufficiently smooth solutions decay polynomially at infinity, and that this decay rate is, in some sense, optimal. The stabilization result for abstract evolution equations is also applied to study the asymptotic behaviour of various systems of partial differential equations.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s00028-002-8083-0", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136368", 
        "issn": [
          "1424-3199", 
          "1424-3202"
        ], 
        "name": "Journal of Evolution Equations", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "2"
      }
    ], 
    "name": "Indirect internal stabilization of weakly coupled evolution equations", 
    "pagination": "127-150", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "7e7b915e0c71af3275a357b7f09c229221766b2a955550ea1956f2b3b61eb171"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00028-002-8083-0"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1026549559"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00028-002-8083-0", 
      "https://app.dimensions.ai/details/publication/pub.1026549559"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T21:40", 
    "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_8687_00000532.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs00028-002-8083-0"
  }
]
 

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/s00028-002-8083-0'

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/s00028-002-8083-0'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00028-002-8083-0'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00028-002-8083-0'


 

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

103 TRIPLES      21 PREDICATES      34 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00028-002-8083-0 schema:about anzsrc-for:01
2 anzsrc-for:0102
3 schema:author N3343f39c8822452dbe368a87bee35cf2
4 schema:citation sg:pub.10.1007/s002330010042
5 https://doi.org/10.1006/jmaa.1993.1071
6 https://doi.org/10.1006/jmaa.1999.6678
7 https://doi.org/10.1016/0022-0396(75)90009-1
8 https://doi.org/10.1016/s0764-4442(99)80316-4
9 https://doi.org/10.1137/0318022
10 https://doi.org/10.1137/s0363012997317505
11 schema:datePublished 2002-05
12 schema:datePublishedReg 2002-05-01
13 schema:description Let two second order evolution equations be coupled via the zero order terms, and suppose that the first one is stabilized by a distributed feedback. What will then be the effect of such a partial stabilization on the decay of solutions at infinity? Is the behaviour of the first component sufficient to stabilize the second one? The answer given in this paper is that sufficiently smooth solutions decay polynomially at infinity, and that this decay rate is, in some sense, optimal. The stabilization result for abstract evolution equations is also applied to study the asymptotic behaviour of various systems of partial differential equations.
14 schema:genre research_article
15 schema:inLanguage en
16 schema:isAccessibleForFree false
17 schema:isPartOf Nd248336be8cb4e9e93f7401ddda24dfb
18 Ne6ba887b23ff44b0a3e29c7fcce5fba0
19 sg:journal.1136368
20 schema:name Indirect internal stabilization of weakly coupled evolution equations
21 schema:pagination 127-150
22 schema:productId N4eb9beb634074621927dacccb3e333d0
23 N60899d46957c4c49be205f2850787dd9
24 Naa6bd293e84a4720a0d72866a9ae2db0
25 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026549559
26 https://doi.org/10.1007/s00028-002-8083-0
27 schema:sdDatePublished 2019-04-10T21:40
28 schema:sdLicense https://scigraph.springernature.com/explorer/license/
29 schema:sdPublisher N87b7b2dcfd094008abac52412c80a07b
30 schema:url http://link.springer.com/10.1007%2Fs00028-002-8083-0
31 sgo:license sg:explorer/license/
32 sgo:sdDataset articles
33 rdf:type schema:ScholarlyArticle
34 N3343f39c8822452dbe368a87bee35cf2 rdf:first sg:person.014476532013.27
35 rdf:rest Nebf6730705eb415a86ccedd001577c14
36 N4eb9beb634074621927dacccb3e333d0 schema:name readcube_id
37 schema:value 7e7b915e0c71af3275a357b7f09c229221766b2a955550ea1956f2b3b61eb171
38 rdf:type schema:PropertyValue
39 N60899d46957c4c49be205f2850787dd9 schema:name doi
40 schema:value 10.1007/s00028-002-8083-0
41 rdf:type schema:PropertyValue
42 N87b7b2dcfd094008abac52412c80a07b schema:name Springer Nature - SN SciGraph project
43 rdf:type schema:Organization
44 Naa6bd293e84a4720a0d72866a9ae2db0 schema:name dimensions_id
45 schema:value pub.1026549559
46 rdf:type schema:PropertyValue
47 Nd248336be8cb4e9e93f7401ddda24dfb schema:issueNumber 2
48 rdf:type schema:PublicationIssue
49 Ne6ba887b23ff44b0a3e29c7fcce5fba0 schema:volumeNumber 2
50 rdf:type schema:PublicationVolume
51 Ne8f519b64e634d88893a5ab98d25fd8d rdf:first sg:person.013053062253.94
52 rdf:rest rdf:nil
53 Nebf6730705eb415a86ccedd001577c14 rdf:first sg:person.014257010655.09
54 rdf:rest Ne8f519b64e634d88893a5ab98d25fd8d
55 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
56 schema:name Mathematical Sciences
57 rdf:type schema:DefinedTerm
58 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
59 schema:name Applied Mathematics
60 rdf:type schema:DefinedTerm
61 sg:journal.1136368 schema:issn 1424-3199
62 1424-3202
63 schema:name Journal of Evolution Equations
64 rdf:type schema:Periodical
65 sg:person.013053062253.94 schema:affiliation https://www.grid.ac/institutes/grid.469947.1
66 schema:familyName Komornik
67 schema:givenName V.
68 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013053062253.94
69 rdf:type schema:Person
70 sg:person.014257010655.09 schema:affiliation https://www.grid.ac/institutes/grid.6530.0
71 schema:familyName Cannarsa
72 schema:givenName P.
73 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014257010655.09
74 rdf:type schema:Person
75 sg:person.014476532013.27 schema:affiliation https://www.grid.ac/institutes/grid.29172.3f
76 schema:familyName Alabau
77 schema:givenName F.
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014476532013.27
79 rdf:type schema:Person
80 sg:pub.10.1007/s002330010042 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030090666
81 https://doi.org/10.1007/s002330010042
82 rdf:type schema:CreativeWork
83 https://doi.org/10.1006/jmaa.1993.1071 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033914765
84 rdf:type schema:CreativeWork
85 https://doi.org/10.1006/jmaa.1999.6678 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042865492
86 rdf:type schema:CreativeWork
87 https://doi.org/10.1016/0022-0396(75)90009-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006374149
88 rdf:type schema:CreativeWork
89 https://doi.org/10.1016/s0764-4442(99)80316-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014128701
90 rdf:type schema:CreativeWork
91 https://doi.org/10.1137/0318022 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062843520
92 rdf:type schema:CreativeWork
93 https://doi.org/10.1137/s0363012997317505 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062881341
94 rdf:type schema:CreativeWork
95 https://www.grid.ac/institutes/grid.29172.3f schema:alternateName University of Lorraine
96 schema:name Département de Mathématique, Université de Metz, Ile du Saulcy, 57000 Metz, France,, FR
97 rdf:type schema:Organization
98 https://www.grid.ac/institutes/grid.469947.1 schema:alternateName Institut de Recherche Mathématique Avancée
99 schema:name Institut de Recherche Mathématique Avancée, Université Louis Pasteur et CNRS, 7, rue René Descartes, 67084 Strasbourg Cedex, France, FR
100 rdf:type schema:Organization
101 https://www.grid.ac/institutes/grid.6530.0 schema:alternateName University of Rome Tor Vergata
102 schema:name Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Roma, Italy, e-mail: cannarsa@axp.mat.uniroma2.it, IT
103 rdf:type schema:Organization
 




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


...