Existence to nonlinear parabolic problems with unbounded weights View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-03

AUTHORS

Iwona Chlebicka, Anna Zatorska-Goldstein

ABSTRACT

We consider the weighted parabolic problem of the type ut-div(ω2(x)|∇u|p-2∇u)=λω1(x)|u|p-2u,x∈Ω,u(x,0)=f(x),x∈Ω,u(x,t)=0,x∈∂Ω,t>0,for quite a general class of possibly unbounded weights ω1,ω2 satisfying the Hardy-type inequality. We prove existence of a global weak solution in the weighted Sobolev spaces provided that λ>0 is smaller than the optimal constant in the inequality. The domain is assumed to be bounded or quasibounded. The obtained solution is proven to belong to Lp(R+;W(ω1,ω2),01,p(Ω))∩L∞(R+;L2(Ω)). More... »

PAGES

1-19

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00028-018-0465-z

DOI

http://dx.doi.org/10.1007/s00028-018-0465-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1106542341


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/2008/0103", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Numerical and Computational 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": "Institute of Mathematics", 
          "id": "https://www.grid.ac/institutes/grid.425010.2", 
          "name": [
            "Institute of Mathematics, Polish Academy of Sciences, ul. \u015aniadeckich 8, 00-656, Warsaw, Poland"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Chlebicka", 
        "givenName": "Iwona", 
        "id": "sg:person.0745416770.54", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0745416770.54"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Warsaw", 
          "id": "https://www.grid.ac/institutes/grid.12847.38", 
          "name": [
            "Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Zatorska-Goldstein", 
        "givenName": "Anna", 
        "id": "sg:person.014722035340.08", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014722035340.08"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s00030-009-0048-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004744364", 
          "https://doi.org/10.1007/s00030-009-0048-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00030-009-0048-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004744364", 
          "https://doi.org/10.1007/s00030-009-0048-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00030-009-0048-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004744364", 
          "https://doi.org/10.1007/s00030-009-0048-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02788144", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005821750", 
          "https://doi.org/10.1007/bf02788144"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02788144", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005821750", 
          "https://doi.org/10.1007/bf02788144"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.anihpc.2013.01.003", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005838418"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jfan.1996.3040", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008108946"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.na.2015.07.016", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010162356"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0362-546x(92)90023-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014556235"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00028-014-0259-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019486682", 
          "https://doi.org/10.1007/s00028-014-0259-x"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jdeq.1997.3375", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023322059"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9947-1984-0742415-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023402342"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1006/jfan.1999.3556", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027703494"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.na.2013.07.006", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036120214"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01766148", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045523591", 
          "https://doi.org/10.1007/bf01766148"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01766148", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045523591", 
          "https://doi.org/10.1007/bf01766148"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01762360", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053563935", 
          "https://doi.org/10.1007/bf01762360"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01762360", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1053563935", 
          "https://doi.org/10.1007/bf01762360"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9947-2015-06125-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059336248"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s0036141003432353", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062875979"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/2044999", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069710924"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-03", 
    "datePublishedReg": "2019-03-01", 
    "description": "We consider the weighted parabolic problem of the type ut-div(\u03c92(x)|\u2207u|p-2\u2207u)=\u03bb\u03c91(x)|u|p-2u,x\u2208\u03a9,u(x,0)=f(x),x\u2208\u03a9,u(x,t)=0,x\u2208\u2202\u03a9,t>0,for quite a general class of possibly unbounded weights \u03c91,\u03c92 satisfying the Hardy-type inequality. We prove existence of a global weak solution in the weighted Sobolev spaces provided that \u03bb>0 is smaller than the optimal constant in the inequality. The domain is assumed to be bounded or quasibounded. The obtained solution is proven to belong to Lp(R+;W(\u03c91,\u03c92),01,p(\u03a9))\u2229L\u221e(R+;L2(\u03a9)).", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s00028-018-0465-z", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1136368", 
        "issn": [
          "1424-3199", 
          "1424-3202"
        ], 
        "name": "Journal of Evolution Equations", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "19"
      }
    ], 
    "name": "Existence to nonlinear parabolic problems with unbounded weights", 
    "pagination": "1-19", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "b2b6ad80718f7de85c854a548cf5a0ebd67af68919e6ed3039f19c51064f1c41"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00028-018-0465-z"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1106542341"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00028-018-0465-z", 
      "https://app.dimensions.ai/details/publication/pub.1106542341"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T10:35", 
    "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/v90/0000000349_0000000349/records_113667_00000005.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs00028-018-0465-z"
  }
]
 

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/s00028-018-0465-z'

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/s00028-018-0465-z'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00028-018-0465-z'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00028-018-0465-z'


 

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

124 TRIPLES      21 PREDICATES      43 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00028-018-0465-z schema:about anzsrc-for:01
2 anzsrc-for:0103
3 schema:author Nac9f3fc6bfde49c6a8217b44de95c425
4 schema:citation sg:pub.10.1007/bf01762360
5 sg:pub.10.1007/bf01766148
6 sg:pub.10.1007/bf02788144
7 sg:pub.10.1007/s00028-014-0259-x
8 sg:pub.10.1007/s00030-009-0048-3
9 https://doi.org/10.1006/jdeq.1997.3375
10 https://doi.org/10.1006/jfan.1996.3040
11 https://doi.org/10.1006/jfan.1999.3556
12 https://doi.org/10.1016/0362-546x(92)90023-8
13 https://doi.org/10.1016/j.anihpc.2013.01.003
14 https://doi.org/10.1016/j.na.2013.07.006
15 https://doi.org/10.1016/j.na.2015.07.016
16 https://doi.org/10.1090/s0002-9947-1984-0742415-3
17 https://doi.org/10.1090/s0002-9947-2015-06125-x
18 https://doi.org/10.1137/s0036141003432353
19 https://doi.org/10.2307/2044999
20 schema:datePublished 2019-03
21 schema:datePublishedReg 2019-03-01
22 schema:description We consider the weighted parabolic problem of the type ut-div(ω2(x)|∇u|p-2∇u)=λω1(x)|u|p-2u,x∈Ω,u(x,0)=f(x),x∈Ω,u(x,t)=0,x∈∂Ω,t>0,for quite a general class of possibly unbounded weights ω1,ω2 satisfying the Hardy-type inequality. We prove existence of a global weak solution in the weighted Sobolev spaces provided that λ>0 is smaller than the optimal constant in the inequality. The domain is assumed to be bounded or quasibounded. The obtained solution is proven to belong to Lp(R+;W(ω1,ω2),01,p(Ω))∩L∞(R+;L2(Ω)).
23 schema:genre research_article
24 schema:inLanguage en
25 schema:isAccessibleForFree true
26 schema:isPartOf N80a3467a445f4cb68927a8dcd6215344
27 Nc2d992b8ee7441f3877cda46d8188a68
28 sg:journal.1136368
29 schema:name Existence to nonlinear parabolic problems with unbounded weights
30 schema:pagination 1-19
31 schema:productId N9c6ea9a737a64dc9bb08249e831a29a0
32 Na78a6b7225534913be17c0e00debe582
33 Nd685a8d5273b498482e1949a4ce1e753
34 schema:sameAs https://app.dimensions.ai/details/publication/pub.1106542341
35 https://doi.org/10.1007/s00028-018-0465-z
36 schema:sdDatePublished 2019-04-11T10:35
37 schema:sdLicense https://scigraph.springernature.com/explorer/license/
38 schema:sdPublisher N63c8d0ea5c48427f8f2c8b2fba831602
39 schema:url https://link.springer.com/10.1007%2Fs00028-018-0465-z
40 sgo:license sg:explorer/license/
41 sgo:sdDataset articles
42 rdf:type schema:ScholarlyArticle
43 N63c8d0ea5c48427f8f2c8b2fba831602 schema:name Springer Nature - SN SciGraph project
44 rdf:type schema:Organization
45 N80a3467a445f4cb68927a8dcd6215344 schema:issueNumber 1
46 rdf:type schema:PublicationIssue
47 N94adeddd83a6428cb5ac0c0939c5091c rdf:first sg:person.014722035340.08
48 rdf:rest rdf:nil
49 N9c6ea9a737a64dc9bb08249e831a29a0 schema:name readcube_id
50 schema:value b2b6ad80718f7de85c854a548cf5a0ebd67af68919e6ed3039f19c51064f1c41
51 rdf:type schema:PropertyValue
52 Na78a6b7225534913be17c0e00debe582 schema:name dimensions_id
53 schema:value pub.1106542341
54 rdf:type schema:PropertyValue
55 Nac9f3fc6bfde49c6a8217b44de95c425 rdf:first sg:person.0745416770.54
56 rdf:rest N94adeddd83a6428cb5ac0c0939c5091c
57 Nc2d992b8ee7441f3877cda46d8188a68 schema:volumeNumber 19
58 rdf:type schema:PublicationVolume
59 Nd685a8d5273b498482e1949a4ce1e753 schema:name doi
60 schema:value 10.1007/s00028-018-0465-z
61 rdf:type schema:PropertyValue
62 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
63 schema:name Mathematical Sciences
64 rdf:type schema:DefinedTerm
65 anzsrc-for:0103 schema:inDefinedTermSet anzsrc-for:
66 schema:name Numerical and Computational Mathematics
67 rdf:type schema:DefinedTerm
68 sg:journal.1136368 schema:issn 1424-3199
69 1424-3202
70 schema:name Journal of Evolution Equations
71 rdf:type schema:Periodical
72 sg:person.014722035340.08 schema:affiliation https://www.grid.ac/institutes/grid.12847.38
73 schema:familyName Zatorska-Goldstein
74 schema:givenName Anna
75 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014722035340.08
76 rdf:type schema:Person
77 sg:person.0745416770.54 schema:affiliation https://www.grid.ac/institutes/grid.425010.2
78 schema:familyName Chlebicka
79 schema:givenName Iwona
80 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0745416770.54
81 rdf:type schema:Person
82 sg:pub.10.1007/bf01762360 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053563935
83 https://doi.org/10.1007/bf01762360
84 rdf:type schema:CreativeWork
85 sg:pub.10.1007/bf01766148 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045523591
86 https://doi.org/10.1007/bf01766148
87 rdf:type schema:CreativeWork
88 sg:pub.10.1007/bf02788144 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005821750
89 https://doi.org/10.1007/bf02788144
90 rdf:type schema:CreativeWork
91 sg:pub.10.1007/s00028-014-0259-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1019486682
92 https://doi.org/10.1007/s00028-014-0259-x
93 rdf:type schema:CreativeWork
94 sg:pub.10.1007/s00030-009-0048-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004744364
95 https://doi.org/10.1007/s00030-009-0048-3
96 rdf:type schema:CreativeWork
97 https://doi.org/10.1006/jdeq.1997.3375 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023322059
98 rdf:type schema:CreativeWork
99 https://doi.org/10.1006/jfan.1996.3040 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008108946
100 rdf:type schema:CreativeWork
101 https://doi.org/10.1006/jfan.1999.3556 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027703494
102 rdf:type schema:CreativeWork
103 https://doi.org/10.1016/0362-546x(92)90023-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014556235
104 rdf:type schema:CreativeWork
105 https://doi.org/10.1016/j.anihpc.2013.01.003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005838418
106 rdf:type schema:CreativeWork
107 https://doi.org/10.1016/j.na.2013.07.006 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036120214
108 rdf:type schema:CreativeWork
109 https://doi.org/10.1016/j.na.2015.07.016 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010162356
110 rdf:type schema:CreativeWork
111 https://doi.org/10.1090/s0002-9947-1984-0742415-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023402342
112 rdf:type schema:CreativeWork
113 https://doi.org/10.1090/s0002-9947-2015-06125-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1059336248
114 rdf:type schema:CreativeWork
115 https://doi.org/10.1137/s0036141003432353 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062875979
116 rdf:type schema:CreativeWork
117 https://doi.org/10.2307/2044999 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069710924
118 rdf:type schema:CreativeWork
119 https://www.grid.ac/institutes/grid.12847.38 schema:alternateName University of Warsaw
120 schema:name Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland
121 rdf:type schema:Organization
122 https://www.grid.ac/institutes/grid.425010.2 schema:alternateName Institute of Mathematics
123 schema:name Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656, Warsaw, Poland
124 rdf:type schema:Organization
 




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


...