The blow-up phenomenon for degenerate parabolic equations with variable coefficients and nonlinear source
The Cauchy problem for a degenerate parabolic equation with a source and variable coefficient of the form ∂ u ∂ t = d i v ( ρ ( x ) u m − 1 | D u | λ − 1 D u ) + u p is studied. Global in time existence and nonexistence conditions are found for a solution to the Cauchy problem. Exact estimates of a...
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| Veröffentlicht in: | Nonlinear analysis 2010-10, Vol.73 (7), p.2310-2323 |
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| container_title | Nonlinear analysis |
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| creator | Cianci, P. Martynenko, A.V. Tedeev, A.F. |
| description | The Cauchy problem for a degenerate parabolic equation with a source and variable coefficient of the form
∂
u
∂
t
=
d
i
v
(
ρ
(
x
)
u
m
−
1
|
D
u
|
λ
−
1
D
u
)
+
u
p
is studied. Global in time existence and nonexistence conditions are found for a solution to the Cauchy problem. Exact estimates of a solution are obtained in the case of global solvability. A sharp universal (i.e., independent of the initial function) estimate of a solution near the blow-up time is obtained. |
| doi_str_mv | 10.1016/j.na.2010.06.026 |
| format | Article |
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∂
u
∂
t
=
d
i
v
(
ρ
(
x
)
u
m
−
1
|
D
u
|
λ
−
1
D
u
)
+
u
p
is studied. Global in time existence and nonexistence conditions are found for a solution to the Cauchy problem. Exact estimates of a solution are obtained in the case of global solvability. A sharp universal (i.e., independent of the initial function) estimate of a solution near the blow-up time is obtained.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2010.06.026</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>Blow-up solution ; Cauchy problem ; Degenerate parabolic equation ; Estimates ; Exact sciences and technology ; Existence and nonexistence theorems ; Mathematical analysis ; Mathematics ; Nonlinearity ; Partial differential equations ; Sciences and techniques of general use ; Source term ; Variable coefficients</subject><ispartof>Nonlinear analysis, 2010-10, Vol.73 (7), p.2310-2323</ispartof><rights>2010 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c357t-2d6ce777fd2fbb851026038862acda42c1557bcc3d322d01187d5331ca11f8d33</citedby><cites>FETCH-LOGICAL-c357t-2d6ce777fd2fbb851026038862acda42c1557bcc3d322d01187d5331ca11f8d33</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.2010.06.026$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23060338$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Cianci, P.</creatorcontrib><creatorcontrib>Martynenko, A.V.</creatorcontrib><creatorcontrib>Tedeev, A.F.</creatorcontrib><title>The blow-up phenomenon for degenerate parabolic equations with variable coefficients and nonlinear source</title><title>Nonlinear analysis</title><description>The Cauchy problem for a degenerate parabolic equation with a source and variable coefficient of the form
∂
u
∂
t
=
d
i
v
(
ρ
(
x
)
u
m
−
1
|
D
u
|
λ
−
1
D
u
)
+
u
p
is studied. Global in time existence and nonexistence conditions are found for a solution to the Cauchy problem. Exact estimates of a solution are obtained in the case of global solvability. A sharp universal (i.e., independent of the initial function) estimate of a solution near the blow-up time is obtained.</description><subject>Blow-up solution</subject><subject>Cauchy problem</subject><subject>Degenerate parabolic equation</subject><subject>Estimates</subject><subject>Exact sciences and technology</subject><subject>Existence and nonexistence theorems</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Nonlinearity</subject><subject>Partial differential equations</subject><subject>Sciences and techniques of general use</subject><subject>Source term</subject><subject>Variable coefficients</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp1UE1LJDEQDcsu7Kzr3WMuC156zMd0utmbiO4KghcX9haqKxUnQ0_SJt2K_94MI948FEXBe6_ee4ydSbGWQpqL3TrCWol6CrMWynxhK9l3ummVbL-yldBGNe3G_P_OfpSyE0LITpsVCw9b4sOYXppl4tOWYtrXidynzB09UqQMM_EJMgxpDMjpaYE5pFj4S5i3_BlygGEkjom8DxgozoVDdLyqjCESZF7SkpF-sm8exkKn7_uE_bu5frj629zd_7m9urxrULfd3ChnkLqu8075YehbWbMI3fdGATrYKJRt2w2I2mmlnJA1pGu1lghS-t5pfcLOj7pTTk8LldnuQ0EaR4iUlmKlMqbbbHSvKlQcoZhTKZm8nXLYQ361UthDq3ZnI9hDq1YYW51Uyq93dSgIo88QMZQPntKiutV9xf0-4qhGfQ6UbTl0g-RCJpytS-HzJ28OMo0v</recordid><startdate>20101001</startdate><enddate>20101001</enddate><creator>Cianci, P.</creator><creator>Martynenko, A.V.</creator><creator>Tedeev, A.F.</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>20101001</creationdate><title>The blow-up phenomenon for degenerate parabolic equations with variable coefficients and nonlinear source</title><author>Cianci, P. ; Martynenko, A.V. ; Tedeev, A.F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c357t-2d6ce777fd2fbb851026038862acda42c1557bcc3d322d01187d5331ca11f8d33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Blow-up solution</topic><topic>Cauchy problem</topic><topic>Degenerate parabolic equation</topic><topic>Estimates</topic><topic>Exact sciences and technology</topic><topic>Existence and nonexistence theorems</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Nonlinearity</topic><topic>Partial differential equations</topic><topic>Sciences and techniques of general use</topic><topic>Source term</topic><topic>Variable coefficients</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cianci, P.</creatorcontrib><creatorcontrib>Martynenko, A.V.</creatorcontrib><creatorcontrib>Tedeev, A.F.</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>Cianci, P.</au><au>Martynenko, A.V.</au><au>Tedeev, A.F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The blow-up phenomenon for degenerate parabolic equations with variable coefficients and nonlinear source</atitle><jtitle>Nonlinear analysis</jtitle><date>2010-10-01</date><risdate>2010</risdate><volume>73</volume><issue>7</issue><spage>2310</spage><epage>2323</epage><pages>2310-2323</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>The Cauchy problem for a degenerate parabolic equation with a source and variable coefficient of the form
∂
u
∂
t
=
d
i
v
(
ρ
(
x
)
u
m
−
1
|
D
u
|
λ
−
1
D
u
)
+
u
p
is studied. Global in time existence and nonexistence conditions are found for a solution to the Cauchy problem. Exact estimates of a solution are obtained in the case of global solvability. A sharp universal (i.e., independent of the initial function) estimate of a solution near the blow-up time is obtained.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2010.06.026</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0362-546X |
| ispartof | Nonlinear analysis, 2010-10, Vol.73 (7), p.2310-2323 |
| issn | 0362-546X 1873-5215 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1266744382 |
| source | Elsevier ScienceDirect Journals |
| subjects | Blow-up solution Cauchy problem Degenerate parabolic equation Estimates Exact sciences and technology Existence and nonexistence theorems Mathematical analysis Mathematics Nonlinearity Partial differential equations Sciences and techniques of general use Source term Variable coefficients |
| title | The blow-up phenomenon for degenerate parabolic equations with variable coefficients and nonlinear source |
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