A priori growth estimates for nonnegative supertemperatures and solutions of semilinear heat equations in a Lipschitz domain
In a bounded Lipschitz domain, we give a priori growth estimates near the parabolic boundary for a certain class of nonnegative supertemperatures which includes nonnegative continuous solutions of semilinear heat equations of the form ∂ t u ( x , t ) − Δ u ( x , t ) = V ( x , t ) u p ( x , t ) , whe...
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| Veröffentlicht in: | Journal d'analyse mathématique (Jerusalem) 2019-07, Vol.138 (1), p.441-463 |
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| container_title | Journal d'analyse mathématique (Jerusalem) |
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| creator | Hirata, Kentaro |
| description | In a bounded Lipschitz domain, we give a priori growth estimates near the parabolic boundary for a certain class of nonnegative supertemperatures which includes nonnegative continuous solutions of semilinear heat equations of the form
∂
t
u
(
x
,
t
)
−
Δ
u
(
x
,
t
)
=
V
(
x
,
t
)
u
p
(
x
,
t
)
,
where
V
(
x, t
) and
p
(
x, t
) are nonnegative Borel measurable functions satisfying weak conditions. A growth rate and the range of
p
depend on the shape of a domain. Our estimates make improvements to a priori estimates given by Bidaut-Véron (1998), Poláčik–Quittner–Souplet (2007) and Taliaferro (2007, 2011). Also, the
C
1
-regularity with respect to the spatial variables and a pointwise gradient estimate are shown. |
| doi_str_mv | 10.1007/s11854-019-0046-2 |
| format | Article |
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∂
t
u
(
x
,
t
)
−
Δ
u
(
x
,
t
)
=
V
(
x
,
t
)
u
p
(
x
,
t
)
,
where
V
(
x, t
) and
p
(
x, t
) are nonnegative Borel measurable functions satisfying weak conditions. A growth rate and the range of
p
depend on the shape of a domain. Our estimates make improvements to a priori estimates given by Bidaut-Véron (1998), Poláčik–Quittner–Souplet (2007) and Taliaferro (2007, 2011). Also, the
C
1
-regularity with respect to the spatial variables and a pointwise gradient estimate are shown.</description><identifier>ISSN: 0021-7670</identifier><identifier>EISSN: 1565-8538</identifier><identifier>DOI: 10.1007/s11854-019-0046-2</identifier><language>eng</language><publisher>Jerusalem: The Hebrew University Magnes Press</publisher><subject>Abstract Harmonic Analysis ; Analysis ; Dynamical Systems and Ergodic Theory ; Estimates ; Functional Analysis ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Partial Differential Equations ; Thermodynamics</subject><ispartof>Journal d'analyse mathématique (Jerusalem), 2019-07, Vol.138 (1), p.441-463</ispartof><rights>The Hebrew University of Jerusalem 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c382t-e8bb776a461a4f6c01ffe25f0c426de74819d9199a939a0f140dec20d048b0613</citedby><cites>FETCH-LOGICAL-c382t-e8bb776a461a4f6c01ffe25f0c426de74819d9199a939a0f140dec20d048b0613</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11854-019-0046-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11854-019-0046-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Hirata, Kentaro</creatorcontrib><title>A priori growth estimates for nonnegative supertemperatures and solutions of semilinear heat equations in a Lipschitz domain</title><title>Journal d'analyse mathématique (Jerusalem)</title><addtitle>JAMA</addtitle><description>In a bounded Lipschitz domain, we give a priori growth estimates near the parabolic boundary for a certain class of nonnegative supertemperatures which includes nonnegative continuous solutions of semilinear heat equations of the form
∂
t
u
(
x
,
t
)
−
Δ
u
(
x
,
t
)
=
V
(
x
,
t
)
u
p
(
x
,
t
)
,
where
V
(
x, t
) and
p
(
x, t
) are nonnegative Borel measurable functions satisfying weak conditions. A growth rate and the range of
p
depend on the shape of a domain. Our estimates make improvements to a priori estimates given by Bidaut-Véron (1998), Poláčik–Quittner–Souplet (2007) and Taliaferro (2007, 2011). Also, the
C
1
-regularity with respect to the spatial variables and a pointwise gradient estimate are shown.</description><subject>Abstract Harmonic Analysis</subject><subject>Analysis</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Estimates</subject><subject>Functional Analysis</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial Differential Equations</subject><subject>Thermodynamics</subject><issn>0021-7670</issn><issn>1565-8538</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LBDEMhosouK7-AG8Fz6Np56s9ivgFC170XLoz6W6XnXZsO4rij7cygicvySHPm5CHkHMGlwygvYqMiboqgMkCoGoKfkAWrG7qQtSlOCQLAM6KtmnhmJzEuAOoa1nyBfm6pmOwPli6Cf49bSnGZAedMFLjA3XeOdzoZN-QxmnEkHDIVacpZEK7nka_n5L1LlJvaMTB7q1DHegWdaL4Oul5aB3VdGXH2G1t-qS9H7R1p-TI6H3Es9--JC93t883D8Xq6f7x5npVdKXgqUCxXrdto6uG6co0HTBjkNcGuoo3PbaVYLKXTEotS6nBsAp67Dj0UIk1NKxckot57xj865Q_VDs_BZdPKs5bASJLkpliM9UFH2NAo7KZQYcPxUD9SFazZJUlqx_JiucMnzMxs26D4W_z_6Fv87yB1A</recordid><startdate>20190701</startdate><enddate>20190701</enddate><creator>Hirata, Kentaro</creator><general>The Hebrew University Magnes Press</general><general>Springer Nature B.V</general><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>20190701</creationdate><title>A priori growth estimates for nonnegative supertemperatures and solutions of semilinear heat equations in a Lipschitz domain</title><author>Hirata, Kentaro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c382t-e8bb776a461a4f6c01ffe25f0c426de74819d9199a939a0f140dec20d048b0613</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Analysis</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Estimates</topic><topic>Functional Analysis</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial Differential Equations</topic><topic>Thermodynamics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hirata, Kentaro</creatorcontrib><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>Journal d'analyse mathématique (Jerusalem)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hirata, Kentaro</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A priori growth estimates for nonnegative supertemperatures and solutions of semilinear heat equations in a Lipschitz domain</atitle><jtitle>Journal d'analyse mathématique (Jerusalem)</jtitle><stitle>JAMA</stitle><date>2019-07-01</date><risdate>2019</risdate><volume>138</volume><issue>1</issue><spage>441</spage><epage>463</epage><pages>441-463</pages><issn>0021-7670</issn><eissn>1565-8538</eissn><abstract>In a bounded Lipschitz domain, we give a priori growth estimates near the parabolic boundary for a certain class of nonnegative supertemperatures which includes nonnegative continuous solutions of semilinear heat equations of the form
∂
t
u
(
x
,
t
)
−
Δ
u
(
x
,
t
)
=
V
(
x
,
t
)
u
p
(
x
,
t
)
,
where
V
(
x, t
) and
p
(
x, t
) are nonnegative Borel measurable functions satisfying weak conditions. A growth rate and the range of
p
depend on the shape of a domain. Our estimates make improvements to a priori estimates given by Bidaut-Véron (1998), Poláčik–Quittner–Souplet (2007) and Taliaferro (2007, 2011). Also, the
C
1
-regularity with respect to the spatial variables and a pointwise gradient estimate are shown.</abstract><cop>Jerusalem</cop><pub>The Hebrew University Magnes Press</pub><doi>10.1007/s11854-019-0046-2</doi><tpages>23</tpages></addata></record> |
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| identifier | ISSN: 0021-7670 |
| ispartof | Journal d'analyse mathématique (Jerusalem), 2019-07, Vol.138 (1), p.441-463 |
| issn | 0021-7670 1565-8538 |
| language | eng |
| recordid | cdi_proquest_journals_2278088539 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Abstract Harmonic Analysis Analysis Dynamical Systems and Ergodic Theory Estimates Functional Analysis Mathematical analysis Mathematics Mathematics and Statistics Partial Differential Equations Thermodynamics |
| title | A priori growth estimates for nonnegative supertemperatures and solutions of semilinear heat equations in a Lipschitz domain |
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