Energy decay for wave equations with nonlinear damping and space-time coefficient in Rn
In this paper, we consider the following nonlinear wave equation u t t − Δ u + a ( t , x ) | u t | m − 1 u t + | u | p − 1 u = 0 , t > 0 , x ∈ R n u ( 0 , x ) = u 0 ( x ) , u t ( 0 , x ) = u 1 ( x ) x ∈ R n and obtain optimal energy decay estimates under suitable assumptions on the space-time non...
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| Veröffentlicht in: | Nonlinearity 2023-03, Vol.36 (3), p.1989-2000 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
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| container_end_page | 2000 |
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| container_issue | 3 |
| container_start_page | 1989 |
| container_title | Nonlinearity |
| container_volume | 36 |
| creator | Ogbiyele, Paul A Arawomo, Peter O |
| description | In this paper, we consider the following nonlinear wave equation
u
t
t
−
Δ
u
+
a
(
t
,
x
)
|
u
t
|
m
−
1
u
t
+
|
u
|
p
−
1
u
=
0
,
t
>
0
,
x
∈
R
n
u
(
0
,
x
)
=
u
0
(
x
)
,
u
t
(
0
,
x
)
=
u
1
(
x
)
x
∈
R
n
and obtain optimal energy decay estimates under suitable assumptions on the space-time nonlinear damping coefficient
a
, where
m
satisfies
1
<
m
⩽
n
+
2
n
−
2
. We establish a new Liapunov type function to obtain energy decay estimates in the case of nonlinear damping instead of the Kormonik lemma. |
| doi_str_mv | 10.1088/1361-6544/acb7c3 |
| format | Article |
| fullrecord | <record><control><sourceid>iop_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1088_1361_6544_acb7c3</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>nonacb7c3</sourcerecordid><originalsourceid>FETCH-LOGICAL-c210t-7f241740ebbce546389740d9eb6fc60459f1a65c4ef851c7e02e0ecfa64ea6623</originalsourceid><addsrcrecordid>eNp1kMFKAzEQhoMoWKt3j3kA1ya7SXb3KKVaoSCI4jHMZic1pZusydbSt7dLxZunn_mZbxg-Qm45u-esqma8UDxTUogZmKY0xRmZ_FXnZMJqybOy5PKSXKW0YYzzKi8m5GPhMa4PtEUDB2pDpHv4RopfOxhc8Inu3fBJffBb5xEibaHrnV9T8C1NPRjMBtchNQGtdcahH6jz9NVfkwsL24Q3vzkl74-Lt_kyW708Pc8fVpnJORuy0uaCl4Jh0xiUQhVVfZzaGhtljWJC1paDkkagrSQ3JbIcGRoLSiAolRdTwk53TQwpRbS6j66DeNCc6VGMHi3o0YI-iTkidyfEhV5vwi7644P_r_8AsLBlwQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Energy decay for wave equations with nonlinear damping and space-time coefficient in Rn</title><source>IOP Publishing Journals</source><source>Institute of Physics (IOP) Journals - HEAL-Link</source><creator>Ogbiyele, Paul A ; Arawomo, Peter O</creator><creatorcontrib>Ogbiyele, Paul A ; Arawomo, Peter O</creatorcontrib><description>In this paper, we consider the following nonlinear wave equation
u
t
t
−
Δ
u
+
a
(
t
,
x
)
|
u
t
|
m
−
1
u
t
+
|
u
|
p
−
1
u
=
0
,
t
>
0
,
x
∈
R
n
u
(
0
,
x
)
=
u
0
(
x
)
,
u
t
(
0
,
x
)
=
u
1
(
x
)
x
∈
R
n
and obtain optimal energy decay estimates under suitable assumptions on the space-time nonlinear damping coefficient
a
, where
m
satisfies
1
<
m
⩽
n
+
2
n
−
2
. We establish a new Liapunov type function to obtain energy decay estimates in the case of nonlinear damping instead of the Kormonik lemma.</description><identifier>ISSN: 0951-7715</identifier><identifier>EISSN: 1361-6544</identifier><identifier>DOI: 10.1088/1361-6544/acb7c3</identifier><identifier>CODEN: NONLE5</identifier><language>eng</language><publisher>IOP Publishing</publisher><subject>35B40 ; 35L05 ; 93D15 ; damping potential ; energy decay ; wave equation</subject><ispartof>Nonlinearity, 2023-03, Vol.36 (3), p.1989-2000</ispartof><rights>2023 IOP Publishing Ltd & London Mathematical Society</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c210t-7f241740ebbce546389740d9eb6fc60459f1a65c4ef851c7e02e0ecfa64ea6623</citedby><cites>FETCH-LOGICAL-c210t-7f241740ebbce546389740d9eb6fc60459f1a65c4ef851c7e02e0ecfa64ea6623</cites><orcidid>0000-0003-1612-0069</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://iopscience.iop.org/article/10.1088/1361-6544/acb7c3/pdf$$EPDF$$P50$$Giop$$H</linktopdf><link.rule.ids>314,780,784,27924,27925,53846,53893</link.rule.ids></links><search><creatorcontrib>Ogbiyele, Paul A</creatorcontrib><creatorcontrib>Arawomo, Peter O</creatorcontrib><title>Energy decay for wave equations with nonlinear damping and space-time coefficient in Rn</title><title>Nonlinearity</title><addtitle>Non</addtitle><addtitle>Nonlinearity</addtitle><description>In this paper, we consider the following nonlinear wave equation
u
t
t
−
Δ
u
+
a
(
t
,
x
)
|
u
t
|
m
−
1
u
t
+
|
u
|
p
−
1
u
=
0
,
t
>
0
,
x
∈
R
n
u
(
0
,
x
)
=
u
0
(
x
)
,
u
t
(
0
,
x
)
=
u
1
(
x
)
x
∈
R
n
and obtain optimal energy decay estimates under suitable assumptions on the space-time nonlinear damping coefficient
a
, where
m
satisfies
1
<
m
⩽
n
+
2
n
−
2
. We establish a new Liapunov type function to obtain energy decay estimates in the case of nonlinear damping instead of the Kormonik lemma.</description><subject>35B40</subject><subject>35L05</subject><subject>93D15</subject><subject>damping potential</subject><subject>energy decay</subject><subject>wave equation</subject><issn>0951-7715</issn><issn>1361-6544</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kMFKAzEQhoMoWKt3j3kA1ya7SXb3KKVaoSCI4jHMZic1pZusydbSt7dLxZunn_mZbxg-Qm45u-esqma8UDxTUogZmKY0xRmZ_FXnZMJqybOy5PKSXKW0YYzzKi8m5GPhMa4PtEUDB2pDpHv4RopfOxhc8Inu3fBJffBb5xEibaHrnV9T8C1NPRjMBtchNQGtdcahH6jz9NVfkwsL24Q3vzkl74-Lt_kyW708Pc8fVpnJORuy0uaCl4Jh0xiUQhVVfZzaGhtljWJC1paDkkagrSQ3JbIcGRoLSiAolRdTwk53TQwpRbS6j66DeNCc6VGMHi3o0YI-iTkidyfEhV5vwi7644P_r_8AsLBlwQ</recordid><startdate>20230301</startdate><enddate>20230301</enddate><creator>Ogbiyele, Paul A</creator><creator>Arawomo, Peter O</creator><general>IOP Publishing</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-1612-0069</orcidid></search><sort><creationdate>20230301</creationdate><title>Energy decay for wave equations with nonlinear damping and space-time coefficient in Rn</title><author>Ogbiyele, Paul A ; Arawomo, Peter O</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c210t-7f241740ebbce546389740d9eb6fc60459f1a65c4ef851c7e02e0ecfa64ea6623</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>35B40</topic><topic>35L05</topic><topic>93D15</topic><topic>damping potential</topic><topic>energy decay</topic><topic>wave equation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ogbiyele, Paul A</creatorcontrib><creatorcontrib>Arawomo, Peter O</creatorcontrib><collection>CrossRef</collection><jtitle>Nonlinearity</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ogbiyele, Paul A</au><au>Arawomo, Peter O</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Energy decay for wave equations with nonlinear damping and space-time coefficient in Rn</atitle><jtitle>Nonlinearity</jtitle><stitle>Non</stitle><addtitle>Nonlinearity</addtitle><date>2023-03-01</date><risdate>2023</risdate><volume>36</volume><issue>3</issue><spage>1989</spage><epage>2000</epage><pages>1989-2000</pages><issn>0951-7715</issn><eissn>1361-6544</eissn><coden>NONLE5</coden><abstract>In this paper, we consider the following nonlinear wave equation
u
t
t
−
Δ
u
+
a
(
t
,
x
)
|
u
t
|
m
−
1
u
t
+
|
u
|
p
−
1
u
=
0
,
t
>
0
,
x
∈
R
n
u
(
0
,
x
)
=
u
0
(
x
)
,
u
t
(
0
,
x
)
=
u
1
(
x
)
x
∈
R
n
and obtain optimal energy decay estimates under suitable assumptions on the space-time nonlinear damping coefficient
a
, where
m
satisfies
1
<
m
⩽
n
+
2
n
−
2
. We establish a new Liapunov type function to obtain energy decay estimates in the case of nonlinear damping instead of the Kormonik lemma.</abstract><pub>IOP Publishing</pub><doi>10.1088/1361-6544/acb7c3</doi><tpages>12</tpages><orcidid>https://orcid.org/0000-0003-1612-0069</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0951-7715 |
| ispartof | Nonlinearity, 2023-03, Vol.36 (3), p.1989-2000 |
| issn | 0951-7715 1361-6544 |
| language | eng |
| recordid | cdi_crossref_primary_10_1088_1361_6544_acb7c3 |
| source | IOP Publishing Journals; Institute of Physics (IOP) Journals - HEAL-Link |
| subjects | 35B40 35L05 93D15 damping potential energy decay wave equation |
| title | Energy decay for wave equations with nonlinear damping and space-time coefficient in Rn |
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