Ontology type: schema:ScholarlyArticle Open Access: True
2021-12-20
AUTHORSH. M. Serag, Abd-Allah Hyder, M. El-Badawy
ABSTRACTIn this work, the elliptic 2×2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$2\times 2$\end{document} cooperative systems involving fractional Laplace operators are studied. Due to the nonlocality of the fractional Laplace operator, we reformulate the problem into a local problem by an extension problem. Then, the existence and uniqueness of the weak solution for these systems are proved. Hence, the existence and optimality conditions are deduced. More... »
PAGES196
http://scigraph.springernature.com/pub.10.1186/s13660-021-02727-3
DOIhttp://dx.doi.org/10.1186/s13660-021-02727-3
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1144048890
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/2008/01",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Mathematical Sciences",
"type": "DefinedTerm"
},
{
"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"
}
],
"author": [
{
"affiliation": {
"alternateName": "Department of Mathematics, Faculty of Sciences, Al-Azhar University, 71524, Cairo, Egypt",
"id": "http://www.grid.ac/institutes/grid.411303.4",
"name": [
"Department of Mathematics, Faculty of Sciences, Al-Azhar University, 71524, Cairo, Egypt"
],
"type": "Organization"
},
"familyName": "Serag",
"givenName": "H. M.",
"id": "sg:person.016272766553.68",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016272766553.68"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, Cairo, Egypt",
"id": "http://www.grid.ac/institutes/grid.411303.4",
"name": [
"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, 61413, Abha, Saudi Arabia",
"Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, Cairo, Egypt"
],
"type": "Organization"
},
"familyName": "Hyder",
"givenName": "Abd-Allah",
"id": "sg:person.015704070103.48",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015704070103.48"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Department of Mathematics, Faculty of Sciences, Al-Azhar University, 71524, Cairo, Egypt",
"id": "http://www.grid.ac/institutes/grid.411303.4",
"name": [
"Department of Mathematics, Faculty of Sciences, Al-Azhar University, 71524, Cairo, Egypt"
],
"type": "Organization"
},
"familyName": "El-Badawy",
"givenName": "M.",
"id": "sg:person.011102735673.75",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011102735673.75"
],
"type": "Person"
}
],
"citation": [
{
"id": "sg:pub.10.1186/s13661-019-1127-y",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1111498769",
"https://doi.org/10.1186/s13661-019-1127-y"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-1-4020-8839-1_3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1005304980",
"https://doi.org/10.1007/978-1-4020-8839-1_3"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10883-009-9067-y",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1006036682",
"https://doi.org/10.1007/s10883-009-9067-y"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s11401-017-1089-2",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1084031408",
"https://doi.org/10.1007/s11401-017-1089-2"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-540-71483-5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1039851741",
"https://doi.org/10.1007/978-3-540-71483-5"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10915-018-0703-0",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1101825279",
"https://doi.org/10.1007/s10915-018-0703-0"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1186/s13662-020-02698-7",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1127866794",
"https://doi.org/10.1186/s13662-020-02698-7"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-65217-2",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1018496323",
"https://doi.org/10.1007/978-3-642-65217-2"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-65024-6",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1109710393",
"https://doi.org/10.1007/978-3-642-65024-6"
],
"type": "CreativeWork"
}
],
"datePublished": "2021-12-20",
"datePublishedReg": "2021-12-20",
"description": "In this work, the elliptic 2\u00d72\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$2\\times 2$\\end{document} cooperative systems involving fractional Laplace operators are studied. Due to the nonlocality of the fractional Laplace operator, we reformulate the problem into a local problem by an extension problem. Then, the existence and uniqueness of the weak solution for these systems are proved. Hence, the existence and optimality conditions are deduced.",
"genre": "article",
"id": "sg:pub.10.1186/s13660-021-02727-3",
"inLanguage": "en",
"isAccessibleForFree": true,
"isPartOf": [
{
"id": "sg:journal.1136856",
"issn": [
"1025-5834",
"1029-242X"
],
"name": "Journal of Inequalities and Applications",
"publisher": "Springer Nature",
"type": "Periodical"
},
{
"issueNumber": "1",
"type": "PublicationIssue"
},
{
"type": "PublicationVolume",
"volumeNumber": "2021"
}
],
"keywords": [
"fractional Laplace operator",
"Laplace operator",
"optimal control",
"optimality conditions",
"weak solutions",
"extension problem",
"cooperative system",
"operators",
"local problems",
"problem",
"existence",
"uniqueness",
"nonlocality",
"system",
"solution",
"work",
"conditions",
"control"
],
"name": "Optimal control for cooperative systems involving fractional Laplace operators",
"pagination": "196",
"productId": [
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1144048890"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1186/s13660-021-02727-3"
]
}
],
"sameAs": [
"https://doi.org/10.1186/s13660-021-02727-3",
"https://app.dimensions.ai/details/publication/pub.1144048890"
],
"sdDataset": "articles",
"sdDatePublished": "2022-05-20T07:39",
"sdLicense": "https://scigraph.springernature.com/explorer/license/",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-springernature-scigraph/baseset/20220519/entities/gbq_results/article/article_912.jsonl",
"type": "ScholarlyArticle",
"url": "https://doi.org/10.1186/s13660-021-02727-3"
}
]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.10.1186/s13660-021-02727-3'
N-Triples is a line-based linked data format ideal for batch operations.
curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1186/s13660-021-02727-3'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1186/s13660-021-02727-3'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1186/s13660-021-02727-3'
This table displays all metadata directly associated to this object as RDF triples.
129 TRIPLES
22 PREDICATES
52 URIs
35 LITERALS
6 BLANK NODES