Longtime Dynamics of a Semilinear Lamé System
This paper is concerned with longtime dynamics of semilinear Lamé systems ∂ t 2 u - μ Δ u - ( λ + μ ) ∇ div u + α ∂ t u + f ( u ) = b , defined in bounded domains of R 3 with Dirichlet boundary condition. Firstly, we establish the existence of finite dimensional global attractors subjected to a crit...
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| Veröffentlicht in: | Journal of dynamics and differential equations 2023-06, Vol.35 (2), p.1435-1456 |
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| container_issue | 2 |
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| container_title | Journal of dynamics and differential equations |
| container_volume | 35 |
| creator | Bocanegra-Rodríguez, Lito Edinson Silva, Marcio Antonio Jorge Ma, To Fu Seminario-Huertas, Paulo Nicanor |
| description | This paper is concerned with longtime dynamics of semilinear Lamé systems
∂
t
2
u
-
μ
Δ
u
-
(
λ
+
μ
)
∇
div
u
+
α
∂
t
u
+
f
(
u
)
=
b
,
defined in bounded domains of
R
3
with Dirichlet boundary condition. Firstly, we establish the existence of finite dimensional global attractors subjected to a critical forcing
f
(
u
). Writing
λ
+
μ
as a positive parameter
ε
, we discuss some physical aspects of the limit case
ε
→
0
. Then, we show the upper-semicontinuity of attractors with respect to the parameter when
ε
→
0
. To our best knowledge, the analysis of attractors for dynamics of Lamé systems has not been studied before. |
| doi_str_mv | 10.1007/s10884-021-09955-7 |
| format | Article |
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∂
t
2
u
-
μ
Δ
u
-
(
λ
+
μ
)
∇
div
u
+
α
∂
t
u
+
f
(
u
)
=
b
,
defined in bounded domains of
R
3
with Dirichlet boundary condition. Firstly, we establish the existence of finite dimensional global attractors subjected to a critical forcing
f
(
u
). Writing
λ
+
μ
as a positive parameter
ε
, we discuss some physical aspects of the limit case
ε
→
0
. Then, we show the upper-semicontinuity of attractors with respect to the parameter when
ε
→
0
. To our best knowledge, the analysis of attractors for dynamics of Lamé systems has not been studied before.</description><identifier>ISSN: 1040-7294</identifier><identifier>EISSN: 1572-9222</identifier><identifier>DOI: 10.1007/s10884-021-09955-7</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Applications of Mathematics ; Boundary conditions ; Dirichlet problem ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations ; Parameters ; Partial Differential Equations</subject><ispartof>Journal of dynamics and differential equations, 2023-06, Vol.35 (2), p.1435-1456</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021</rights><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-3599329862bb38b6bdd22fdb974a162515d83fc4718335872dffdd4c9655277f3</citedby><cites>FETCH-LOGICAL-c319t-3599329862bb38b6bdd22fdb974a162515d83fc4718335872dffdd4c9655277f3</cites><orcidid>0000-0002-9467-1299</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10884-021-09955-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10884-021-09955-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Bocanegra-Rodríguez, Lito Edinson</creatorcontrib><creatorcontrib>Silva, Marcio Antonio Jorge</creatorcontrib><creatorcontrib>Ma, To Fu</creatorcontrib><creatorcontrib>Seminario-Huertas, Paulo Nicanor</creatorcontrib><title>Longtime Dynamics of a Semilinear Lamé System</title><title>Journal of dynamics and differential equations</title><addtitle>J Dyn Diff Equat</addtitle><description>This paper is concerned with longtime dynamics of semilinear Lamé systems
∂
t
2
u
-
μ
Δ
u
-
(
λ
+
μ
)
∇
div
u
+
α
∂
t
u
+
f
(
u
)
=
b
,
defined in bounded domains of
R
3
with Dirichlet boundary condition. Firstly, we establish the existence of finite dimensional global attractors subjected to a critical forcing
f
(
u
). Writing
λ
+
μ
as a positive parameter
ε
, we discuss some physical aspects of the limit case
ε
→
0
. Then, we show the upper-semicontinuity of attractors with respect to the parameter when
ε
→
0
. To our best knowledge, the analysis of attractors for dynamics of Lamé systems has not been studied before.</description><subject>Applications of Mathematics</subject><subject>Boundary conditions</subject><subject>Dirichlet problem</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><subject>Parameters</subject><subject>Partial Differential Equations</subject><issn>1040-7294</issn><issn>1572-9222</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kLFOwzAURS0EEqXwA0yRmF3sZzv2G1GBghSJoTBbTmJXqZqk2OnQT-I7-DECQWJjene45z7pEHLN2YIzpm8TZ8ZIyoBThqgU1SdkxpUGigBwOmYmGdWA8pxcpLRljKEROCOLou82Q9P67P7YubapUtaHzGVr3za7pvMuZoVrPz-y9TENvr0kZ8Htkr_6vXPy9vjwunyixcvqeXlX0EpwHKhQiALQ5FCWwpR5WdcAoS5RS8dzUFzVRoRKam6EUEZDHUJdywpzpUDrIObkZtrdx_794NNgt_0hduNLC4aj5EoYHFswtarYpxR9sPvYtC4eLWf224udvNjRi_3xYvUIiQlKY7nb-Pg3_Q_1BaKjY-c</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Bocanegra-Rodríguez, Lito Edinson</creator><creator>Silva, Marcio Antonio Jorge</creator><creator>Ma, To Fu</creator><creator>Seminario-Huertas, Paulo Nicanor</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-9467-1299</orcidid></search><sort><creationdate>20230601</creationdate><title>Longtime Dynamics of a Semilinear Lamé System</title><author>Bocanegra-Rodríguez, Lito Edinson ; Silva, Marcio Antonio Jorge ; Ma, To Fu ; Seminario-Huertas, Paulo Nicanor</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-3599329862bb38b6bdd22fdb974a162515d83fc4718335872dffdd4c9655277f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Applications of Mathematics</topic><topic>Boundary conditions</topic><topic>Dirichlet problem</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equations</topic><topic>Parameters</topic><topic>Partial Differential Equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bocanegra-Rodríguez, Lito Edinson</creatorcontrib><creatorcontrib>Silva, Marcio Antonio Jorge</creatorcontrib><creatorcontrib>Ma, To Fu</creatorcontrib><creatorcontrib>Seminario-Huertas, Paulo Nicanor</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of dynamics and differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bocanegra-Rodríguez, Lito Edinson</au><au>Silva, Marcio Antonio Jorge</au><au>Ma, To Fu</au><au>Seminario-Huertas, Paulo Nicanor</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Longtime Dynamics of a Semilinear Lamé System</atitle><jtitle>Journal of dynamics and differential equations</jtitle><stitle>J Dyn Diff Equat</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>35</volume><issue>2</issue><spage>1435</spage><epage>1456</epage><pages>1435-1456</pages><issn>1040-7294</issn><eissn>1572-9222</eissn><abstract>This paper is concerned with longtime dynamics of semilinear Lamé systems
∂
t
2
u
-
μ
Δ
u
-
(
λ
+
μ
)
∇
div
u
+
α
∂
t
u
+
f
(
u
)
=
b
,
defined in bounded domains of
R
3
with Dirichlet boundary condition. Firstly, we establish the existence of finite dimensional global attractors subjected to a critical forcing
f
(
u
). Writing
λ
+
μ
as a positive parameter
ε
, we discuss some physical aspects of the limit case
ε
→
0
. Then, we show the upper-semicontinuity of attractors with respect to the parameter when
ε
→
0
. To our best knowledge, the analysis of attractors for dynamics of Lamé systems has not been studied before.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10884-021-09955-7</doi><tpages>22</tpages><orcidid>https://orcid.org/0000-0002-9467-1299</orcidid></addata></record> |
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| identifier | ISSN: 1040-7294 |
| ispartof | Journal of dynamics and differential equations, 2023-06, Vol.35 (2), p.1435-1456 |
| issn | 1040-7294 1572-9222 |
| language | eng |
| recordid | cdi_proquest_journals_2819415389 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Applications of Mathematics Boundary conditions Dirichlet problem Mathematics Mathematics and Statistics Ordinary Differential Equations Parameters Partial Differential Equations |
| title | Longtime Dynamics of a Semilinear Lamé System |
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