General decay rates for the wave equation with mixed-type damping mechanisms on unbounded domain with finite measure
This paper is concerned with the study of the uniform decay rates of the energy associated with the wave equation subject to a locally distributed viscoelastic dissipation and a nonlinear frictional damping u t t - Δ u + ∫ 0 t g ( t - s ) div [ a ( x ) ∇ u ( s ) ] d s + b ( x ) f ( u t ) = 0 on Ω ×...
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| Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Physik 2015-12, Vol.66 (6), p.3123-3145 |
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| container_title | Zeitschrift für angewandte Mathematik und Physik |
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| creator | Dias Silva, Flávio R. Nascimento, Flávio A. F. Rodrigues, José H. |
| description | This paper is concerned with the study of the uniform decay rates of the energy associated with the wave equation subject to a locally distributed viscoelastic dissipation and a nonlinear frictional damping
u
t
t
-
Δ
u
+
∫
0
t
g
(
t
-
s
)
div
[
a
(
x
)
∇
u
(
s
)
]
d
s
+
b
(
x
)
f
(
u
t
)
=
0
on
Ω
×
]
0
,
∞
[
,
where
Ω
⊂
R
n
,
n
≥
2
is an
unbounded
open set with
finite measure
and unbounded smooth boundary
∂
Ω
=
Γ
. Supposing that the localization functions satisfy the “competitive” assumption
a
(
x
)
+
b
(
x
)
≥
δ
>
0
for all
x
∈
Ω
and the relaxation function
g
satisfies certain nonlinear differential inequalities introduced by Lasiecka et al. (J Math Phys 54(3):031504,
2013
), we extend to our considered domain the prior results of Cavalcanti and Oquendo (SIAM J Control Optim 42(4):1310–1324,
2003
). In addition, while in Cavalcanti and Oquendo (
2003
) the authors just consider exponential and polynomial decay rate estimates, in the present article general decay rate estimates are obtained. |
| doi_str_mv | 10.1007/s00033-015-0547-5 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1808060990</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1808060990</sourcerecordid><originalsourceid>FETCH-LOGICAL-c321t-63b7c6a23b20963ba76d4c55b2be2a6ef94d795663d2f8621031578b5bed2f533</originalsourceid><addsrcrecordid>eNp9kLFOwzAQhi0EEqXwAGweWQxnO06aEVVQkCqxwGw58aV11Tit7VD69rgqM9PpTt9_0v8Rcs_hkQNUTxEApGTAFQNVVExdkAkvBLAaZH1JJgBFwYSo1DW5iXGT6YqDnJC0QI_BbKnF1hxpMAkj7YZA0xrpwXwjxf1okhs8Pbi0pr37QcvScYfUmn7n_Ir22K6Nd7GPNFOjb4bRW7TUDr1xf7HOeZcwoyaOAW_JVWe2Ee_-5pR8vb58zt_Y8mPxPn9eslYKnlgpm6otjZCNgDovpipt0SrViAaFKbGrC1vVqiylFd2sFLkQV9WsUQ3mg5JySh7Of3dh2I8Yk-5dbHG7NR6HMWo-gxmUUGdHU8LPaBuGGAN2ehdcb8JRc9Anw_psWGfD-mRYq5wR50zMrF9h0JthDD43-if0C1RGf4I</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1808060990</pqid></control><display><type>article</type><title>General decay rates for the wave equation with mixed-type damping mechanisms on unbounded domain with finite measure</title><source>Springer Nature - Complete Springer Journals</source><creator>Dias Silva, Flávio R. ; Nascimento, Flávio A. F. ; Rodrigues, José H.</creator><creatorcontrib>Dias Silva, Flávio R. ; Nascimento, Flávio A. F. ; Rodrigues, José H.</creatorcontrib><description>This paper is concerned with the study of the uniform decay rates of the energy associated with the wave equation subject to a locally distributed viscoelastic dissipation and a nonlinear frictional damping
u
t
t
-
Δ
u
+
∫
0
t
g
(
t
-
s
)
div
[
a
(
x
)
∇
u
(
s
)
]
d
s
+
b
(
x
)
f
(
u
t
)
=
0
on
Ω
×
]
0
,
∞
[
,
where
Ω
⊂
R
n
,
n
≥
2
is an
unbounded
open set with
finite measure
and unbounded smooth boundary
∂
Ω
=
Γ
. Supposing that the localization functions satisfy the “competitive” assumption
a
(
x
)
+
b
(
x
)
≥
δ
>
0
for all
x
∈
Ω
and the relaxation function
g
satisfies certain nonlinear differential inequalities introduced by Lasiecka et al. (J Math Phys 54(3):031504,
2013
), we extend to our considered domain the prior results of Cavalcanti and Oquendo (SIAM J Control Optim 42(4):1310–1324,
2003
). In addition, while in Cavalcanti and Oquendo (
2003
) the authors just consider exponential and polynomial decay rate estimates, in the present article general decay rate estimates are obtained.</description><identifier>ISSN: 0044-2275</identifier><identifier>EISSN: 1420-9039</identifier><identifier>DOI: 10.1007/s00033-015-0547-5</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Damping ; Decay rate ; Engineering ; Estimates ; Functions (mathematics) ; Mathematical analysis ; Mathematical Methods in Physics ; Nonlinearity ; Polynomials ; Theoretical and Applied Mechanics ; Wave equations</subject><ispartof>Zeitschrift für angewandte Mathematik und Physik, 2015-12, Vol.66 (6), p.3123-3145</ispartof><rights>Springer Basel 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c321t-63b7c6a23b20963ba76d4c55b2be2a6ef94d795663d2f8621031578b5bed2f533</citedby><cites>FETCH-LOGICAL-c321t-63b7c6a23b20963ba76d4c55b2be2a6ef94d795663d2f8621031578b5bed2f533</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00033-015-0547-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00033-015-0547-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Dias Silva, Flávio R.</creatorcontrib><creatorcontrib>Nascimento, Flávio A. F.</creatorcontrib><creatorcontrib>Rodrigues, José H.</creatorcontrib><title>General decay rates for the wave equation with mixed-type damping mechanisms on unbounded domain with finite measure</title><title>Zeitschrift für angewandte Mathematik und Physik</title><addtitle>Z. Angew. Math. Phys</addtitle><description>This paper is concerned with the study of the uniform decay rates of the energy associated with the wave equation subject to a locally distributed viscoelastic dissipation and a nonlinear frictional damping
u
t
t
-
Δ
u
+
∫
0
t
g
(
t
-
s
)
div
[
a
(
x
)
∇
u
(
s
)
]
d
s
+
b
(
x
)
f
(
u
t
)
=
0
on
Ω
×
]
0
,
∞
[
,
where
Ω
⊂
R
n
,
n
≥
2
is an
unbounded
open set with
finite measure
and unbounded smooth boundary
∂
Ω
=
Γ
. Supposing that the localization functions satisfy the “competitive” assumption
a
(
x
)
+
b
(
x
)
≥
δ
>
0
for all
x
∈
Ω
and the relaxation function
g
satisfies certain nonlinear differential inequalities introduced by Lasiecka et al. (J Math Phys 54(3):031504,
2013
), we extend to our considered domain the prior results of Cavalcanti and Oquendo (SIAM J Control Optim 42(4):1310–1324,
2003
). In addition, while in Cavalcanti and Oquendo (
2003
) the authors just consider exponential and polynomial decay rate estimates, in the present article general decay rate estimates are obtained.</description><subject>Damping</subject><subject>Decay rate</subject><subject>Engineering</subject><subject>Estimates</subject><subject>Functions (mathematics)</subject><subject>Mathematical analysis</subject><subject>Mathematical Methods in Physics</subject><subject>Nonlinearity</subject><subject>Polynomials</subject><subject>Theoretical and Applied Mechanics</subject><subject>Wave equations</subject><issn>0044-2275</issn><issn>1420-9039</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9kLFOwzAQhi0EEqXwAGweWQxnO06aEVVQkCqxwGw58aV11Tit7VD69rgqM9PpTt9_0v8Rcs_hkQNUTxEApGTAFQNVVExdkAkvBLAaZH1JJgBFwYSo1DW5iXGT6YqDnJC0QI_BbKnF1hxpMAkj7YZA0xrpwXwjxf1okhs8Pbi0pr37QcvScYfUmn7n_Ir22K6Nd7GPNFOjb4bRW7TUDr1xf7HOeZcwoyaOAW_JVWe2Ee_-5pR8vb58zt_Y8mPxPn9eslYKnlgpm6otjZCNgDovpipt0SrViAaFKbGrC1vVqiylFd2sFLkQV9WsUQ3mg5JySh7Of3dh2I8Yk-5dbHG7NR6HMWo-gxmUUGdHU8LPaBuGGAN2ehdcb8JRc9Anw_psWGfD-mRYq5wR50zMrF9h0JthDD43-if0C1RGf4I</recordid><startdate>20151201</startdate><enddate>20151201</enddate><creator>Dias Silva, Flávio R.</creator><creator>Nascimento, Flávio A. F.</creator><creator>Rodrigues, José H.</creator><general>Springer International Publishing</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>20151201</creationdate><title>General decay rates for the wave equation with mixed-type damping mechanisms on unbounded domain with finite measure</title><author>Dias Silva, Flávio R. ; Nascimento, Flávio A. F. ; Rodrigues, José H.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c321t-63b7c6a23b20963ba76d4c55b2be2a6ef94d795663d2f8621031578b5bed2f533</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Damping</topic><topic>Decay rate</topic><topic>Engineering</topic><topic>Estimates</topic><topic>Functions (mathematics)</topic><topic>Mathematical analysis</topic><topic>Mathematical Methods in Physics</topic><topic>Nonlinearity</topic><topic>Polynomials</topic><topic>Theoretical and Applied Mechanics</topic><topic>Wave equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dias Silva, Flávio R.</creatorcontrib><creatorcontrib>Nascimento, Flávio A. F.</creatorcontrib><creatorcontrib>Rodrigues, José H.</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dias Silva, Flávio R.</au><au>Nascimento, Flávio A. F.</au><au>Rodrigues, José H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>General decay rates for the wave equation with mixed-type damping mechanisms on unbounded domain with finite measure</atitle><jtitle>Zeitschrift für angewandte Mathematik und Physik</jtitle><stitle>Z. Angew. Math. Phys</stitle><date>2015-12-01</date><risdate>2015</risdate><volume>66</volume><issue>6</issue><spage>3123</spage><epage>3145</epage><pages>3123-3145</pages><issn>0044-2275</issn><eissn>1420-9039</eissn><abstract>This paper is concerned with the study of the uniform decay rates of the energy associated with the wave equation subject to a locally distributed viscoelastic dissipation and a nonlinear frictional damping
u
t
t
-
Δ
u
+
∫
0
t
g
(
t
-
s
)
div
[
a
(
x
)
∇
u
(
s
)
]
d
s
+
b
(
x
)
f
(
u
t
)
=
0
on
Ω
×
]
0
,
∞
[
,
where
Ω
⊂
R
n
,
n
≥
2
is an
unbounded
open set with
finite measure
and unbounded smooth boundary
∂
Ω
=
Γ
. Supposing that the localization functions satisfy the “competitive” assumption
a
(
x
)
+
b
(
x
)
≥
δ
>
0
for all
x
∈
Ω
and the relaxation function
g
satisfies certain nonlinear differential inequalities introduced by Lasiecka et al. (J Math Phys 54(3):031504,
2013
), we extend to our considered domain the prior results of Cavalcanti and Oquendo (SIAM J Control Optim 42(4):1310–1324,
2003
). In addition, while in Cavalcanti and Oquendo (
2003
) the authors just consider exponential and polynomial decay rate estimates, in the present article general decay rate estimates are obtained.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00033-015-0547-5</doi><tpages>23</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0044-2275 |
| ispartof | Zeitschrift für angewandte Mathematik und Physik, 2015-12, Vol.66 (6), p.3123-3145 |
| issn | 0044-2275 1420-9039 |
| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Damping Decay rate Engineering Estimates Functions (mathematics) Mathematical analysis Mathematical Methods in Physics Nonlinearity Polynomials Theoretical and Applied Mechanics Wave equations |
| title | General decay rates for the wave equation with mixed-type damping mechanisms on unbounded domain with finite measure |
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