Blow-up results and global existence of positive solutions for the inhomogeneous evolution P-Laplacian equations
This paper deals with the Cauchy problem of inhomogeneous evolution P-Laplacian equations ∂ t u − div ( | ∇ u | p − 2 ∇ u ) = u q + w ( x ) with nonnegative initial data, where p > 1 , q > max { 1 , p − 1 } , and w ( x ) ⁄ ≡ 0 is a nonnegative continuous functions in R n . We prove that q c =...
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| Veröffentlicht in: | Nonlinear analysis 2007-03, Vol.66 (6), p.1290-1301 |
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| container_title | Nonlinear analysis |
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| creator | Zeng, Xianzhong |
| description | This paper deals with the Cauchy problem of inhomogeneous evolution P-Laplacian equations
∂
t
u
−
div
(
|
∇
u
|
p
−
2
∇
u
)
=
u
q
+
w
(
x
)
with nonnegative initial data, where
p
>
1
,
q
>
max
{
1
,
p
−
1
}
, and
w
(
x
)
⁄
≡
0
is a nonnegative continuous functions in
R
n
. We prove that
q
c
=
(
p
−
1
)
n
/
(
n
−
p
)
is its critical exponent provided that
2
n
/
(
n
+
1
)
<
p
<
n
, i.e., if
q
≤
q
c
, then every positive solution blows up in finite time; whereas for
q
>
q
c
, the equation possesses a global positive solution for some
w
(
x
)
and some initial data. Meanwhile, we also prove that its positive solutions blow up in finite time provided that
n
≤
p
. |
| doi_str_mv | 10.1016/j.na.2006.01.026 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_29107941</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0362546X06000575</els_id><sourcerecordid>29107941</sourcerecordid><originalsourceid>FETCH-LOGICAL-c355t-46da482e8f723d6187d5c936022999e56cd70a0025601c6113eb03b9e620eee53</originalsourceid><addsrcrecordid>eNp1kD2PEzEQhi0EEuGgp3QD3S5jO_bGdHDi46RIUIBEZzne2TtHjr3n2Q3w79lcIl1FNc3zvjPzMPZaQCtAmHf7NvtWApgWRAvSPGErselUo6XQT9kKlJGNXptfz9kLoj0AiE6ZFRs_pvK7mUdekeY0Efe557ep7Hzi-CfShDkgLwMfC8UpHpFTSfMUSyY-lMqnO-Qx35VDucWMZSaOxwvAvzdbPyYfos8c72f_kHrJng0-Eb66zCv28_OnH9dfm-23LzfXH7ZNUFpPzdr0fr2RuBk6qXqzvNLrYJUBKa21qE3oO_AAUhsQwQihcAdqZ9FIQEStrtjbc-9Yy_2MNLlDpIAp-YcznbQCOrsWCwhnMNRCVHFwY40HX_86Ae6k1u1d9u6k1oFwi9ol8ubS7Sn4NFSfQ6TH3EYLqy0s3Pszh8ujx4jVUYgnoX2sGCbXl_j_Jf8ANcWO9g</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>29107941</pqid></control><display><type>article</type><title>Blow-up results and global existence of positive solutions for the inhomogeneous evolution P-Laplacian equations</title><source>Elsevier ScienceDirect Journals</source><creator>Zeng, Xianzhong</creator><creatorcontrib>Zeng, Xianzhong</creatorcontrib><description>This paper deals with the Cauchy problem of inhomogeneous evolution P-Laplacian equations
∂
t
u
−
div
(
|
∇
u
|
p
−
2
∇
u
)
=
u
q
+
w
(
x
)
with nonnegative initial data, where
p
>
1
,
q
>
max
{
1
,
p
−
1
}
, and
w
(
x
)
⁄
≡
0
is a nonnegative continuous functions in
R
n
. We prove that
q
c
=
(
p
−
1
)
n
/
(
n
−
p
)
is its critical exponent provided that
2
n
/
(
n
+
1
)
<
p
<
n
, i.e., if
q
≤
q
c
, then every positive solution blows up in finite time; whereas for
q
>
q
c
, the equation possesses a global positive solution for some
w
(
x
)
and some initial data. Meanwhile, we also prove that its positive solutions blow up in finite time provided that
n
≤
p
.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2006.01.026</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Blow-up ; Critical exponent ; Exact sciences and technology ; Global analysis, analysis on manifolds ; Global existence ; Inhomogeneous evolution P-Laplacian equation ; Mathematical analysis ; Mathematics ; Partial differential equations ; Sciences and techniques of general use ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><ispartof>Nonlinear analysis, 2007-03, Vol.66 (6), p.1290-1301</ispartof><rights>2006 Elsevier Ltd</rights><rights>2007 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-46da482e8f723d6187d5c936022999e56cd70a0025601c6113eb03b9e620eee53</citedby><cites>FETCH-LOGICAL-c355t-46da482e8f723d6187d5c936022999e56cd70a0025601c6113eb03b9e620eee53</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.na.2006.01.026$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18519590$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Zeng, Xianzhong</creatorcontrib><title>Blow-up results and global existence of positive solutions for the inhomogeneous evolution P-Laplacian equations</title><title>Nonlinear analysis</title><description>This paper deals with the Cauchy problem of inhomogeneous evolution P-Laplacian equations
∂
t
u
−
div
(
|
∇
u
|
p
−
2
∇
u
)
=
u
q
+
w
(
x
)
with nonnegative initial data, where
p
>
1
,
q
>
max
{
1
,
p
−
1
}
, and
w
(
x
)
⁄
≡
0
is a nonnegative continuous functions in
R
n
. We prove that
q
c
=
(
p
−
1
)
n
/
(
n
−
p
)
is its critical exponent provided that
2
n
/
(
n
+
1
)
<
p
<
n
, i.e., if
q
≤
q
c
, then every positive solution blows up in finite time; whereas for
q
>
q
c
, the equation possesses a global positive solution for some
w
(
x
)
and some initial data. Meanwhile, we also prove that its positive solutions blow up in finite time provided that
n
≤
p
.</description><subject>Blow-up</subject><subject>Critical exponent</subject><subject>Exact sciences and technology</subject><subject>Global analysis, analysis on manifolds</subject><subject>Global existence</subject><subject>Inhomogeneous evolution P-Laplacian equation</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Partial differential equations</subject><subject>Sciences and techniques of general use</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNp1kD2PEzEQhi0EEuGgp3QD3S5jO_bGdHDi46RIUIBEZzne2TtHjr3n2Q3w79lcIl1FNc3zvjPzMPZaQCtAmHf7NvtWApgWRAvSPGErselUo6XQT9kKlJGNXptfz9kLoj0AiE6ZFRs_pvK7mUdekeY0Efe557ep7Hzi-CfShDkgLwMfC8UpHpFTSfMUSyY-lMqnO-Qx35VDucWMZSaOxwvAvzdbPyYfos8c72f_kHrJng0-Eb66zCv28_OnH9dfm-23LzfXH7ZNUFpPzdr0fr2RuBk6qXqzvNLrYJUBKa21qE3oO_AAUhsQwQihcAdqZ9FIQEStrtjbc-9Yy_2MNLlDpIAp-YcznbQCOrsWCwhnMNRCVHFwY40HX_86Ae6k1u1d9u6k1oFwi9ol8ubS7Sn4NFSfQ6TH3EYLqy0s3Pszh8ujx4jVUYgnoX2sGCbXl_j_Jf8ANcWO9g</recordid><startdate>20070315</startdate><enddate>20070315</enddate><creator>Zeng, Xianzhong</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20070315</creationdate><title>Blow-up results and global existence of positive solutions for the inhomogeneous evolution P-Laplacian equations</title><author>Zeng, Xianzhong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-46da482e8f723d6187d5c936022999e56cd70a0025601c6113eb03b9e620eee53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Blow-up</topic><topic>Critical exponent</topic><topic>Exact sciences and technology</topic><topic>Global analysis, analysis on manifolds</topic><topic>Global existence</topic><topic>Inhomogeneous evolution P-Laplacian equation</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Partial differential equations</topic><topic>Sciences and techniques of general use</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zeng, Xianzhong</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zeng, Xianzhong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Blow-up results and global existence of positive solutions for the inhomogeneous evolution P-Laplacian equations</atitle><jtitle>Nonlinear analysis</jtitle><date>2007-03-15</date><risdate>2007</risdate><volume>66</volume><issue>6</issue><spage>1290</spage><epage>1301</epage><pages>1290-1301</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>This paper deals with the Cauchy problem of inhomogeneous evolution P-Laplacian equations
∂
t
u
−
div
(
|
∇
u
|
p
−
2
∇
u
)
=
u
q
+
w
(
x
)
with nonnegative initial data, where
p
>
1
,
q
>
max
{
1
,
p
−
1
}
, and
w
(
x
)
⁄
≡
0
is a nonnegative continuous functions in
R
n
. We prove that
q
c
=
(
p
−
1
)
n
/
(
n
−
p
)
is its critical exponent provided that
2
n
/
(
n
+
1
)
<
p
<
n
, i.e., if
q
≤
q
c
, then every positive solution blows up in finite time; whereas for
q
>
q
c
, the equation possesses a global positive solution for some
w
(
x
)
and some initial data. Meanwhile, we also prove that its positive solutions blow up in finite time provided that
n
≤
p
.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2006.01.026</doi><tpages>12</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0362-546X |
| ispartof | Nonlinear analysis, 2007-03, Vol.66 (6), p.1290-1301 |
| issn | 0362-546X 1873-5215 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_29107941 |
| source | Elsevier ScienceDirect Journals |
| subjects | Blow-up Critical exponent Exact sciences and technology Global analysis, analysis on manifolds Global existence Inhomogeneous evolution P-Laplacian equation Mathematical analysis Mathematics Partial differential equations Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Blow-up results and global existence of positive solutions for the inhomogeneous evolution P-Laplacian equations |
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