General energy decay for wave equation with space-time potential and time delay in Rn
In this paper, we consider the following wave equation u tt - Δ u + a 0 b ( t , x ) u t + a 1 b ( t , x ) u t ( t - τ ) + | 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 u t ( t - τ , x ) = h 0 ( t - τ , x ) , x ∈ R n , 0 < t < τ , with space...
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| Veröffentlicht in: | Afrika mathematica 2023, Vol.34 (4) |
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| container_title | Afrika mathematica |
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| creator | Ogbiyele, Paul A. Arawomo, Peter O. |
| description | In this paper, we consider the following wave equation
u
tt
-
Δ
u
+
a
0
b
(
t
,
x
)
u
t
+
a
1
b
(
t
,
x
)
u
t
(
t
-
τ
)
+
|
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
u
t
(
t
-
τ
,
x
)
=
h
0
(
t
-
τ
,
x
)
,
x
∈
R
n
,
0
<
t
<
τ
,
with space time dependent potential and a time delay in the internal feedback. Under appropriate conditions on the damping coefficients
b
and the constants
a
0
,
a
1
, we establish a general energy decay result of the solution where the initial data have compact support. |
| doi_str_mv | 10.1007/s13370-023-01120-1 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_sprin</sourceid><recordid>TN_cdi_proquest_journals_2882889887</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2882889887</sourcerecordid><originalsourceid>FETCH-LOGICAL-p157t-6ce2e106c4b6b4aa8f1c63613bea8e8e0374c64bc6b6727400b32fc8ee3f18e63</originalsourceid><addsrcrecordid>eNpFkEFLAzEQhYMoWGr_gKeA5-hMkibpUYrWQkEQew7ZdLZuqdnt7tbSf2_aCg4DD4b35sHH2D3CIwLYpw6VsiBAKgGIEgResYHECQhrjLtmAwSUYqJhfMtGXbeBPNqgGasBW84oURu2_CTrI19RDEde1i0_hB_itNuHvqoTP1T9F--aEEn01Tfxpu4p9VUOhrTi59OKtjlaJf6R7thNGbYdjf50yJavL5_TN7F4n82nzwvR4Nj2wkSShGCiLkyhQ3AlRqMMqoKCI0egrI5GF9EUxkqrAQoly-iIVImOjBqyh8vfpq13e-p6v6n3bcqVXjqXd-KczS51cXVNW6U1tf8uBH9C6C8IfUbozwg9ql_1DGO0</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2882889887</pqid></control><display><type>article</type><title>General energy decay for wave equation with space-time potential and time delay in Rn</title><source>SpringerLink Journals</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 wave equation
u
tt
-
Δ
u
+
a
0
b
(
t
,
x
)
u
t
+
a
1
b
(
t
,
x
)
u
t
(
t
-
τ
)
+
|
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
u
t
(
t
-
τ
,
x
)
=
h
0
(
t
-
τ
,
x
)
,
x
∈
R
n
,
0
<
t
<
τ
,
with space time dependent potential and a time delay in the internal feedback. Under appropriate conditions on the damping coefficients
b
and the constants
a
0
,
a
1
, we establish a general energy decay result of the solution where the initial data have compact support.</description><identifier>ISSN: 1012-9405</identifier><identifier>EISSN: 2190-7668</identifier><identifier>DOI: 10.1007/s13370-023-01120-1</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applications of Mathematics ; Damping ; Decay ; History of Mathematical Sciences ; Mathematics ; Mathematics and Statistics ; Mathematics Education ; Time dependence ; Time lag ; Wave equations</subject><ispartof>Afrika mathematica, 2023, Vol.34 (4)</ispartof><rights>African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000-0003-1612-0069</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/s13370-023-01120-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13370-023-01120-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Ogbiyele, Paul A.</creatorcontrib><creatorcontrib>Arawomo, Peter O.</creatorcontrib><title>General energy decay for wave equation with space-time potential and time delay in Rn</title><title>Afrika mathematica</title><addtitle>Afr. Mat</addtitle><description>In this paper, we consider the following wave equation
u
tt
-
Δ
u
+
a
0
b
(
t
,
x
)
u
t
+
a
1
b
(
t
,
x
)
u
t
(
t
-
τ
)
+
|
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
u
t
(
t
-
τ
,
x
)
=
h
0
(
t
-
τ
,
x
)
,
x
∈
R
n
,
0
<
t
<
τ
,
with space time dependent potential and a time delay in the internal feedback. Under appropriate conditions on the damping coefficients
b
and the constants
a
0
,
a
1
, we establish a general energy decay result of the solution where the initial data have compact support.</description><subject>Applications of Mathematics</subject><subject>Damping</subject><subject>Decay</subject><subject>History of Mathematical Sciences</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics Education</subject><subject>Time dependence</subject><subject>Time lag</subject><subject>Wave equations</subject><issn>1012-9405</issn><issn>2190-7668</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkEFLAzEQhYMoWGr_gKeA5-hMkibpUYrWQkEQew7ZdLZuqdnt7tbSf2_aCg4DD4b35sHH2D3CIwLYpw6VsiBAKgGIEgResYHECQhrjLtmAwSUYqJhfMtGXbeBPNqgGasBW84oURu2_CTrI19RDEde1i0_hB_itNuHvqoTP1T9F--aEEn01Tfxpu4p9VUOhrTi59OKtjlaJf6R7thNGbYdjf50yJavL5_TN7F4n82nzwvR4Nj2wkSShGCiLkyhQ3AlRqMMqoKCI0egrI5GF9EUxkqrAQoly-iIVImOjBqyh8vfpq13e-p6v6n3bcqVXjqXd-KczS51cXVNW6U1tf8uBH9C6C8IfUbozwg9ql_1DGO0</recordid><startdate>2023</startdate><enddate>2023</enddate><creator>Ogbiyele, Paul A.</creator><creator>Arawomo, Peter O.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope/><orcidid>https://orcid.org/0000-0003-1612-0069</orcidid></search><sort><creationdate>2023</creationdate><title>General energy decay for wave equation with space-time potential and time delay in Rn</title><author>Ogbiyele, Paul A. ; Arawomo, Peter O.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p157t-6ce2e106c4b6b4aa8f1c63613bea8e8e0374c64bc6b6727400b32fc8ee3f18e63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Applications of Mathematics</topic><topic>Damping</topic><topic>Decay</topic><topic>History of Mathematical Sciences</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics Education</topic><topic>Time dependence</topic><topic>Time lag</topic><topic>Wave equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ogbiyele, Paul A.</creatorcontrib><creatorcontrib>Arawomo, Peter O.</creatorcontrib><jtitle>Afrika mathematica</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>General energy decay for wave equation with space-time potential and time delay in Rn</atitle><jtitle>Afrika mathematica</jtitle><stitle>Afr. Mat</stitle><date>2023</date><risdate>2023</risdate><volume>34</volume><issue>4</issue><issn>1012-9405</issn><eissn>2190-7668</eissn><abstract>In this paper, we consider the following wave equation
u
tt
-
Δ
u
+
a
0
b
(
t
,
x
)
u
t
+
a
1
b
(
t
,
x
)
u
t
(
t
-
τ
)
+
|
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
u
t
(
t
-
τ
,
x
)
=
h
0
(
t
-
τ
,
x
)
,
x
∈
R
n
,
0
<
t
<
τ
,
with space time dependent potential and a time delay in the internal feedback. Under appropriate conditions on the damping coefficients
b
and the constants
a
0
,
a
1
, we establish a general energy decay result of the solution where the initial data have compact support.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s13370-023-01120-1</doi><orcidid>https://orcid.org/0000-0003-1612-0069</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1012-9405 |
| ispartof | Afrika mathematica, 2023, Vol.34 (4) |
| issn | 1012-9405 2190-7668 |
| language | eng |
| recordid | cdi_proquest_journals_2882889887 |
| source | SpringerLink Journals |
| subjects | Applications of Mathematics Damping Decay History of Mathematical Sciences Mathematics Mathematics and Statistics Mathematics Education Time dependence Time lag Wave equations |
| title | General energy decay for wave equation with space-time potential and time delay in Rn |
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