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Upper semicontinuity of uniform attractors for nonclassical diffusion equations
We study the upper semicontinuity of a uniform attractor for a nonautonomous nonclassical diffusion equation with critical nonlinearity. In particular, we prove that the uniform (with respect to (w.r.t.) g ∈ Σ ) attractor A Σ ε ( ε ⩾ 0 ) for equation ( 1.1 ) satisfies lim ε → ε 0 dist H 0 1 ( Ω ) (...
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| Published in: | Boundary value problems 2017-06, Vol.2017 (1), p.1-11, Article 84 |
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| container_end_page | 11 |
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| container_title | Boundary value problems |
| container_volume | 2017 |
| creator | Wang, Yonghai Li, Pengrui Qin, Yuming |
| description | We study the upper semicontinuity of a uniform attractor for a nonautonomous nonclassical diffusion equation with critical nonlinearity. In particular, we prove that the uniform (with respect to (w.r.t.)
g
∈
Σ
) attractor
A
Σ
ε
(
ε
⩾
0
) for equation (
1.1
) satisfies
lim
ε
→
ε
0
dist
H
0
1
(
Ω
)
(
A
Σ
ε
,
A
Σ
ε
0
)
=
0
for any
ε
0
⩾
0
. |
| doi_str_mv | 10.1186/s13661-017-0816-7 |
| format | article |
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g
∈
Σ
) attractor
A
Σ
ε
(
ε
⩾
0
) for equation (
1.1
) satisfies
lim
ε
→
ε
0
dist
H
0
1
(
Ω
)
(
A
Σ
ε
,
A
Σ
ε
0
)
=
0
for any
ε
0
⩾
0
.</description><identifier>ISSN: 1687-2770</identifier><identifier>ISSN: 1687-2762</identifier><identifier>EISSN: 1687-2770</identifier><identifier>DOI: 10.1186/s13661-017-0816-7</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Approximations and Expansions ; Difference and Functional Equations ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; nonautonomous ; nonclassical diffusion equation ; Nonlinearity ; Ordinary Differential Equations ; Partial Differential Equations ; uniform attractor ; upper semicontinuity</subject><ispartof>Boundary value problems, 2017-06, Vol.2017 (1), p.1-11, Article 84</ispartof><rights>The Author(s) 2017</rights><rights>Boundary Value Problems is a copyright of Springer, 2017.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c425t-dd5ec16bcb7005c271b0a7776d603c8a618dea092c7503dedd7ae6bfa6c3acf03</citedby><cites>FETCH-LOGICAL-c425t-dd5ec16bcb7005c271b0a7776d603c8a618dea092c7503dedd7ae6bfa6c3acf03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/1906358778/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/1906358778?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25752,27923,27924,37011,44589,74897</link.rule.ids></links><search><creatorcontrib>Wang, Yonghai</creatorcontrib><creatorcontrib>Li, Pengrui</creatorcontrib><creatorcontrib>Qin, Yuming</creatorcontrib><title>Upper semicontinuity of uniform attractors for nonclassical diffusion equations</title><title>Boundary value problems</title><addtitle>Bound Value Probl</addtitle><description>We study the upper semicontinuity of a uniform attractor for a nonautonomous nonclassical diffusion equation with critical nonlinearity. In particular, we prove that the uniform (with respect to (w.r.t.)
g
∈
Σ
) attractor
A
Σ
ε
(
ε
⩾
0
) for equation (
1.1
) satisfies
lim
ε
→
ε
0
dist
H
0
1
(
Ω
)
(
A
Σ
ε
,
A
Σ
ε
0
)
=
0
for any
ε
0
⩾
0
.</description><subject>Analysis</subject><subject>Approximations and Expansions</subject><subject>Difference and Functional Equations</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>nonautonomous</subject><subject>nonclassical diffusion equation</subject><subject>Nonlinearity</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><subject>uniform attractor</subject><subject>upper semicontinuity</subject><issn>1687-2770</issn><issn>1687-2762</issn><issn>1687-2770</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNp1UclqwzAQNaWFrh_Qm6Fnt5JlaeRjKd2gkEtzFmMtQSGxEkk-5O-r1KX00tO8Gd4y8KrqlpJ7SqV4SJQJQRtCoSGSigZOqgsqJDQtADn9g8-ry5TWhLCede1FtVjudjbWyW69DmP24-TzoQ6unkbvQtzWmHNEnUNMddnrMYx6gyl5jZvaeOem5MNY2_2EuYB0XZ053CR78zOvquXL8-fTW_OxeH1_evxodNfy3BjDraZi0AMQwnULdCAIAMIIwrREQaWxSPpWAyfMWGMArRgcCs1QO8KuqvfZ1wRcq130W4wHFdCr70OIK4Uxe72xiiHwEsSdRNv1nA4UJWCHnPWOYeeK193stYthP9mU1TpMcSzvK9oTwbgEkIVFZ5aOIaVo3W8qJerYgZo7UKUDdexAQdG0syYV7riy8Y_zv6IvE-KLxA</recordid><startdate>20170606</startdate><enddate>20170606</enddate><creator>Wang, Yonghai</creator><creator>Li, Pengrui</creator><creator>Qin, Yuming</creator><general>Springer International Publishing</general><general>Hindawi Limited</general><general>SpringerOpen</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>DOA</scope></search><sort><creationdate>20170606</creationdate><title>Upper semicontinuity of uniform attractors for nonclassical diffusion equations</title><author>Wang, Yonghai ; Li, Pengrui ; Qin, Yuming</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c425t-dd5ec16bcb7005c271b0a7776d603c8a618dea092c7503dedd7ae6bfa6c3acf03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Analysis</topic><topic>Approximations and Expansions</topic><topic>Difference and Functional Equations</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>nonautonomous</topic><topic>nonclassical diffusion equation</topic><topic>Nonlinearity</topic><topic>Ordinary Differential Equations</topic><topic>Partial Differential Equations</topic><topic>uniform attractor</topic><topic>upper semicontinuity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Yonghai</creatorcontrib><creatorcontrib>Li, Pengrui</creatorcontrib><creatorcontrib>Qin, Yuming</creatorcontrib><collection>SpringerOpen</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Boundary value problems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Yonghai</au><au>Li, Pengrui</au><au>Qin, Yuming</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Upper semicontinuity of uniform attractors for nonclassical diffusion equations</atitle><jtitle>Boundary value problems</jtitle><stitle>Bound Value Probl</stitle><date>2017-06-06</date><risdate>2017</risdate><volume>2017</volume><issue>1</issue><spage>1</spage><epage>11</epage><pages>1-11</pages><artnum>84</artnum><issn>1687-2770</issn><issn>1687-2762</issn><eissn>1687-2770</eissn><abstract>We study the upper semicontinuity of a uniform attractor for a nonautonomous nonclassical diffusion equation with critical nonlinearity. In particular, we prove that the uniform (with respect to (w.r.t.)
g
∈
Σ
) attractor
A
Σ
ε
(
ε
⩾
0
) for equation (
1.1
) satisfies
lim
ε
→
ε
0
dist
H
0
1
(
Ω
)
(
A
Σ
ε
,
A
Σ
ε
0
)
=
0
for any
ε
0
⩾
0
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1186/s13661-017-0816-7</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Boundary value problems, 2017-06, Vol.2017 (1), p.1-11, Article 84 |
| issn | 1687-2770 1687-2762 1687-2770 |
| language | eng |
| recordid | cdi_doaj_primary_oai_doaj_org_article_3a75bcb5f8ae4951b1a87a4a539f3a4f |
| source | Publicly Available Content Database; Springer Nature - SpringerLink Journals - Fully Open Access |
| subjects | Analysis Approximations and Expansions Difference and Functional Equations Mathematical analysis Mathematics Mathematics and Statistics nonautonomous nonclassical diffusion equation Nonlinearity Ordinary Differential Equations Partial Differential Equations uniform attractor upper semicontinuity |
| title | Upper semicontinuity of uniform attractors for nonclassical diffusion equations |
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