Existence and Asymptotic Behavior of Solutions for Degenerate Nonlinear Kirchhoff Strings with Variable-Exponent Nonlinearities
In this paper, we investigate the existence of a local solution in time and discuss the exponential asymptotic behavior to a weakly damped wave equation involving the variable-exponents u t t − M ∇ u t 2 Δ u + ∫ 0 t g t − s Δ u s d s + γ 1 u t + u t k x − 1 u t = u p x − 1 u in Ω × ℝ + with simply s...
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| Veröffentlicht in: | Acta mathematica vietnamica 2021, Vol.46 (3), p.613-643 |
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| container_title | Acta mathematica vietnamica |
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| creator | Abita, Rahmoune |
| description | In this paper, we investigate the existence of a local solution in time and discuss the exponential asymptotic behavior to a weakly damped wave equation involving the variable-exponents
u
t
t
−
M
∇
u
t
2
Δ
u
+
∫
0
t
g
t
−
s
Δ
u
s
d
s
+
γ
1
u
t
+
u
t
k
x
−
1
u
t
=
u
p
x
−
1
u
in
Ω
×
ℝ
+
with simply supported boundary condition, where Ω is a bounded domain of
ℝ
n
,
g
> 0 is a memory kernel that decays exponentially, and
M
(
s
) is a locally Lipschitz function. This kind of problem without the memory term when
k
(.) and
p
(.) are constants models viscoelastic Kirchhoff equation. |
| doi_str_mv | 10.1007/s40306-021-00420-7 |
| format | Article |
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u
t
t
−
M
∇
u
t
2
Δ
u
+
∫
0
t
g
t
−
s
Δ
u
s
d
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γ
1
u
t
+
u
t
k
x
−
1
u
t
=
u
p
x
−
1
u
in
Ω
×
ℝ
+
with simply supported boundary condition, where Ω is a bounded domain of
ℝ
n
,
g
> 0 is a memory kernel that decays exponentially, and
M
(
s
) is a locally Lipschitz function. This kind of problem without the memory term when
k
(.) and
p
(.) are constants models viscoelastic Kirchhoff equation.</description><identifier>ISSN: 0251-4184</identifier><identifier>EISSN: 2315-4144</identifier><identifier>DOI: 10.1007/s40306-021-00420-7</identifier><language>eng</language><publisher>Singapore: Springer Singapore</publisher><subject>Asymptotic properties ; Boundary conditions ; Mathematics ; Mathematics and Statistics ; Nonlinearity ; Wave equations</subject><ispartof>Acta mathematica vietnamica, 2021, Vol.46 (3), p.613-643</ispartof><rights>Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2021</rights><rights>Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2021.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-5ad393242290f56cb53f58bb97e1fb2e5398835fb20a651e03b5d6617e0c612d3</citedby><cites>FETCH-LOGICAL-c319t-5ad393242290f56cb53f58bb97e1fb2e5398835fb20a651e03b5d6617e0c612d3</cites><orcidid>0000-0003-2384-2668</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/s40306-021-00420-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40306-021-00420-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Abita, Rahmoune</creatorcontrib><title>Existence and Asymptotic Behavior of Solutions for Degenerate Nonlinear Kirchhoff Strings with Variable-Exponent Nonlinearities</title><title>Acta mathematica vietnamica</title><addtitle>Acta Math Vietnam</addtitle><description>In this paper, we investigate the existence of a local solution in time and discuss the exponential asymptotic behavior to a weakly damped wave equation involving the variable-exponents
u
t
t
−
M
∇
u
t
2
Δ
u
+
∫
0
t
g
t
−
s
Δ
u
s
d
s
+
γ
1
u
t
+
u
t
k
x
−
1
u
t
=
u
p
x
−
1
u
in
Ω
×
ℝ
+
with simply supported boundary condition, where Ω is a bounded domain of
ℝ
n
,
g
> 0 is a memory kernel that decays exponentially, and
M
(
s
) is a locally Lipschitz function. This kind of problem without the memory term when
k
(.) and
p
(.) are constants models viscoelastic Kirchhoff equation.</description><subject>Asymptotic properties</subject><subject>Boundary conditions</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinearity</subject><subject>Wave equations</subject><issn>0251-4184</issn><issn>2315-4144</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kDtPxDAQhC0EEifgD1BZog6s7dhJSh7HQyAoeLSWk2w4o8MOtg-4ir-Oj0Oio9rRar5Z7RCyz-CQAVRHsQQBqgDOCoCSQ1FtkAkXTBYlK8tNMgEuWdZ1uU32YrQtMFEpqGo5IV_TTxsTug6pcT09jsvXMflkO3qCM_NufaB-oPd-vkjWu0iHvDjDZ3QYTEJ6693cOjSBXtvQzWZ-yOYUrHuO9MOmGX0ywZp2jsX0c_QOXfpDbLIYd8nWYOYR937nDnk8nz6cXhY3dxdXp8c3RSdYkwppetEIXnLewCBV10oxyLptmwrZ0HKUoqlrIbMEoyRDEK3slWIVQqcY78UOOVjnjsG_LTAm_eIXweWTmksplVQ5PLv42tUFH2PAQY_Bvpqw1Az0qmu97lrnrvVP17rKkFhDcVw9juEv-h_qGwpugyM</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Abita, Rahmoune</creator><general>Springer Singapore</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-2384-2668</orcidid></search><sort><creationdate>2021</creationdate><title>Existence and Asymptotic Behavior of Solutions for Degenerate Nonlinear Kirchhoff Strings with Variable-Exponent Nonlinearities</title><author>Abita, Rahmoune</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-5ad393242290f56cb53f58bb97e1fb2e5398835fb20a651e03b5d6617e0c612d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Asymptotic properties</topic><topic>Boundary conditions</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinearity</topic><topic>Wave equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Abita, Rahmoune</creatorcontrib><collection>CrossRef</collection><jtitle>Acta mathematica vietnamica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Abita, Rahmoune</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence and Asymptotic Behavior of Solutions for Degenerate Nonlinear Kirchhoff Strings with Variable-Exponent Nonlinearities</atitle><jtitle>Acta mathematica vietnamica</jtitle><stitle>Acta Math Vietnam</stitle><date>2021</date><risdate>2021</risdate><volume>46</volume><issue>3</issue><spage>613</spage><epage>643</epage><pages>613-643</pages><issn>0251-4184</issn><eissn>2315-4144</eissn><abstract>In this paper, we investigate the existence of a local solution in time and discuss the exponential asymptotic behavior to a weakly damped wave equation involving the variable-exponents
u
t
t
−
M
∇
u
t
2
Δ
u
+
∫
0
t
g
t
−
s
Δ
u
s
d
s
+
γ
1
u
t
+
u
t
k
x
−
1
u
t
=
u
p
x
−
1
u
in
Ω
×
ℝ
+
with simply supported boundary condition, where Ω is a bounded domain of
ℝ
n
,
g
> 0 is a memory kernel that decays exponentially, and
M
(
s
) is a locally Lipschitz function. This kind of problem without the memory term when
k
(.) and
p
(.) are constants models viscoelastic Kirchhoff equation.</abstract><cop>Singapore</cop><pub>Springer Singapore</pub><doi>10.1007/s40306-021-00420-7</doi><tpages>31</tpages><orcidid>https://orcid.org/0000-0003-2384-2668</orcidid></addata></record> |
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| ispartof | Acta mathematica vietnamica, 2021, Vol.46 (3), p.613-643 |
| issn | 0251-4184 2315-4144 |
| language | eng |
| recordid | cdi_proquest_journals_2555656242 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Asymptotic properties Boundary conditions Mathematics Mathematics and Statistics Nonlinearity Wave equations |
| title | Existence and Asymptotic Behavior of Solutions for Degenerate Nonlinear Kirchhoff Strings with Variable-Exponent Nonlinearities |
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