Semigroups of locally Lipschitz operators associated with semilinear evolution equations of parabolic type
A characterization problem is discussed, of semigroups of locally Lipschitz operators providing mild solutions to the Cauchy problem for the semilinear evolution equation of parabolic type u ′ ( t ) = ( A + B ) u ( t ) for t > 0 . By parabolic type we mean that the operator A is the infinitesimal...
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| Veröffentlicht in: | Nonlinear analysis 2008-12, Vol.69 (11), p.4025-4054 |
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| container_title | Nonlinear analysis |
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| creator | Matsumoto, Toshitaka Tanaka, Naoki |
| description | A characterization problem is discussed, of semigroups of locally Lipschitz operators providing mild solutions to the Cauchy problem for the semilinear evolution equation of parabolic type
u
′
(
t
)
=
(
A
+
B
)
u
(
t
)
for
t
>
0
. By parabolic type we mean that the operator
A
is the infinitesimal generator of an analytic
(
C
0
)
semigroup on a general Banach space
X
. The operator
B
is assumed to be locally continuous from a subset of
Y
into
X
, where
Y
is a Banach space which is contained in
X
and has a stronger norm defined through a fractional power of
−
A
. The characterization is applied to the global solvability of the mixed problem for the complex Ginzburg–Landau equation. |
| doi_str_mv | 10.1016/j.na.2007.10.035 |
| format | Article |
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u
′
(
t
)
=
(
A
+
B
)
u
(
t
)
for
t
>
0
. By parabolic type we mean that the operator
A
is the infinitesimal generator of an analytic
(
C
0
)
semigroup on a general Banach space
X
. The operator
B
is assumed to be locally continuous from a subset of
Y
into
X
, where
Y
is a Banach space which is contained in
X
and has a stronger norm defined through a fractional power of
−
A
. The characterization is applied to the global solvability of the mixed problem for the complex Ginzburg–Landau equation.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2007.10.035</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>Analytic semigroup ; Exact sciences and technology ; Finite differences and functional equations ; Fractional power ; Global analysis, analysis on manifolds ; Group theory ; Group theory and generalizations ; Mathematical analysis ; Mathematics ; Mild solution ; Partial differential equations ; Sciences and techniques of general use ; Semigroup of locally Lipschitz operators ; Semilinear evolution equation of parabolic type ; Smoothing effect ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><ispartof>Nonlinear analysis, 2008-12, Vol.69 (11), p.4025-4054</ispartof><rights>2007 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-b426e75ff8cd04de2cf455feaf685139730957d6f9942153c5629071ebb0951a3</citedby><cites>FETCH-LOGICAL-c355t-b426e75ff8cd04de2cf455feaf685139730957d6f9942153c5629071ebb0951a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0362546X07007092$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3536,27903,27904,65309</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20857008$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Matsumoto, Toshitaka</creatorcontrib><creatorcontrib>Tanaka, Naoki</creatorcontrib><title>Semigroups of locally Lipschitz operators associated with semilinear evolution equations of parabolic type</title><title>Nonlinear analysis</title><description>A characterization problem is discussed, of semigroups of locally Lipschitz operators providing mild solutions to the Cauchy problem for the semilinear evolution equation of parabolic type
u
′
(
t
)
=
(
A
+
B
)
u
(
t
)
for
t
>
0
. By parabolic type we mean that the operator
A
is the infinitesimal generator of an analytic
(
C
0
)
semigroup on a general Banach space
X
. The operator
B
is assumed to be locally continuous from a subset of
Y
into
X
, where
Y
is a Banach space which is contained in
X
and has a stronger norm defined through a fractional power of
−
A
. The characterization is applied to the global solvability of the mixed problem for the complex Ginzburg–Landau equation.</description><subject>Analytic semigroup</subject><subject>Exact sciences and technology</subject><subject>Finite differences and functional equations</subject><subject>Fractional power</subject><subject>Global analysis, analysis on manifolds</subject><subject>Group theory</subject><subject>Group theory and generalizations</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mild solution</subject><subject>Partial differential equations</subject><subject>Sciences and techniques of general use</subject><subject>Semigroup of locally Lipschitz operators</subject><subject>Semilinear evolution equation of parabolic type</subject><subject>Smoothing effect</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>2008</creationdate><recordtype>article</recordtype><recordid>eNp1UE1v1DAUtBBILIU7R1_glq0dx3bCDVV8SStxoJV6s946z9Qrb5zaTtH21-OwVW-c3tfMPM0Q8p6zLWdcXR62E2xbxnQdt0zIF2TDey0a2XL5kmyYUG0jO3X7mrzJ-cAY41qoDTn8wqP_neIyZxodDdFCCCe683O2d7480jhjghJTppBztB4KjvSPL3c0V2bwE0Ki-BDDUnycKN4vsDb_1GZIsI_BW1pOM74lrxyEjO-e6gW5-frl-up7s_v57cfV511jhZSl2XetQi2d6-3IuhFb6zopHYJTveRi0IINUo_KDUNXvQkrVTswzXG_rwcO4oJ8POvOKd4vmIs5-mwxBJgwLtkIxVvV674C2RloU8w5oTNz8kdIJ8OZWUM1BzOBWUNdNzXUSvnwpA25JuUSTNbnZ17LeqkZW6U_nXFYjT54TCZbj5PF0Se0xYzR___JX645jbo</recordid><startdate>20081201</startdate><enddate>20081201</enddate><creator>Matsumoto, Toshitaka</creator><creator>Tanaka, Naoki</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>20081201</creationdate><title>Semigroups of locally Lipschitz operators associated with semilinear evolution equations of parabolic type</title><author>Matsumoto, Toshitaka ; Tanaka, Naoki</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-b426e75ff8cd04de2cf455feaf685139730957d6f9942153c5629071ebb0951a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Analytic semigroup</topic><topic>Exact sciences and technology</topic><topic>Finite differences and functional equations</topic><topic>Fractional power</topic><topic>Global analysis, analysis on manifolds</topic><topic>Group theory</topic><topic>Group theory and generalizations</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mild solution</topic><topic>Partial differential equations</topic><topic>Sciences and techniques of general use</topic><topic>Semigroup of locally Lipschitz operators</topic><topic>Semilinear evolution equation of parabolic type</topic><topic>Smoothing effect</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Matsumoto, Toshitaka</creatorcontrib><creatorcontrib>Tanaka, Naoki</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>Matsumoto, Toshitaka</au><au>Tanaka, Naoki</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Semigroups of locally Lipschitz operators associated with semilinear evolution equations of parabolic type</atitle><jtitle>Nonlinear analysis</jtitle><date>2008-12-01</date><risdate>2008</risdate><volume>69</volume><issue>11</issue><spage>4025</spage><epage>4054</epage><pages>4025-4054</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>A characterization problem is discussed, of semigroups of locally Lipschitz operators providing mild solutions to the Cauchy problem for the semilinear evolution equation of parabolic type
u
′
(
t
)
=
(
A
+
B
)
u
(
t
)
for
t
>
0
. By parabolic type we mean that the operator
A
is the infinitesimal generator of an analytic
(
C
0
)
semigroup on a general Banach space
X
. The operator
B
is assumed to be locally continuous from a subset of
Y
into
X
, where
Y
is a Banach space which is contained in
X
and has a stronger norm defined through a fractional power of
−
A
. The characterization is applied to the global solvability of the mixed problem for the complex Ginzburg–Landau equation.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2007.10.035</doi><tpages>30</tpages></addata></record> |
| fulltext | fulltext |
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| ispartof | Nonlinear analysis, 2008-12, Vol.69 (11), p.4025-4054 |
| issn | 0362-546X 1873-5215 |
| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Analytic semigroup Exact sciences and technology Finite differences and functional equations Fractional power Global analysis, analysis on manifolds Group theory Group theory and generalizations Mathematical analysis Mathematics Mild solution Partial differential equations Sciences and techniques of general use Semigroup of locally Lipschitz operators Semilinear evolution equation of parabolic type Smoothing effect Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Semigroups of locally Lipschitz operators associated with semilinear evolution equations of parabolic type |
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