Head and Tail Speeds of Mean Curvature Flow with Forcing
In this paper, we investigate the large time behavior of interfaces moving with motion law V = - κ + g ( x ) , where g is positive, Lipschitz and Z n -periodic. We show that the behavior of the interface can be characterized by its head and tail speeds s ¯ and s ̲ , which only depend on its overall...
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| creator | Gao, Hongwei Kim, Inwon |
| description | In this paper, we investigate the large time behavior of interfaces moving with motion law
V
=
-
κ
+
g
(
x
)
, where
g
is positive, Lipschitz and
Z
n
-periodic. We show that the behavior of the interface can be characterized by its head and tail speeds
s
¯
and
s
̲
, which only depend on its overall direction of propagation
ν
. We discuss the large time behavior of the moving interface in terms of
s
¯
and
s
̲
, which is shown to vary continuously in
ν
. In the laminar setting we show that when
s
¯
>
s
̲
there exists an unbounded stationary solution as well as localized traveling waves with different speeds. |
| doi_str_mv | 10.1007/s00205-019-01423-3 |
| format | Article |
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V
=
-
κ
+
g
(
x
)
, where
g
is positive, Lipschitz and
Z
n
-periodic. We show that the behavior of the interface can be characterized by its head and tail speeds
s
¯
and
s
̲
, which only depend on its overall direction of propagation
ν
. We discuss the large time behavior of the moving interface in terms of
s
¯
and
s
̲
, which is shown to vary continuously in
ν
. In the laminar setting we show that when
s
¯
>
s
̲
there exists an unbounded stationary solution as well as localized traveling waves with different speeds.</description><identifier>ISSN: 0003-9527</identifier><identifier>EISSN: 1432-0673</identifier><identifier>DOI: 10.1007/s00205-019-01423-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Classical Mechanics ; Complex Systems ; Curvature ; Fluid- and Aerodynamics ; Mathematical and Computational Physics ; Physics ; Physics and Astronomy ; Spectrum allocation ; Theoretical ; Traveling waves</subject><ispartof>Archive for rational mechanics and analysis, 2020, Vol.235 (1), p.287-354</ispartof><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2019</rights><rights>Archive for Rational Mechanics and Analysis is a copyright of Springer, (2019). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-e808f0e96a79d0b33973aaa64e6e695b041d434d7428bcd163d439b84cf87caa3</citedby><cites>FETCH-LOGICAL-c319t-e808f0e96a79d0b33973aaa64e6e695b041d434d7428bcd163d439b84cf87caa3</cites><orcidid>0000-0003-2766-589X</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/s00205-019-01423-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00205-019-01423-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Gao, Hongwei</creatorcontrib><creatorcontrib>Kim, Inwon</creatorcontrib><title>Head and Tail Speeds of Mean Curvature Flow with Forcing</title><title>Archive for rational mechanics and analysis</title><addtitle>Arch Rational Mech Anal</addtitle><description>In this paper, we investigate the large time behavior of interfaces moving with motion law
V
=
-
κ
+
g
(
x
)
, where
g
is positive, Lipschitz and
Z
n
-periodic. We show that the behavior of the interface can be characterized by its head and tail speeds
s
¯
and
s
̲
, which only depend on its overall direction of propagation
ν
. We discuss the large time behavior of the moving interface in terms of
s
¯
and
s
̲
, which is shown to vary continuously in
ν
. In the laminar setting we show that when
s
¯
>
s
̲
there exists an unbounded stationary solution as well as localized traveling waves with different speeds.</description><subject>Classical Mechanics</subject><subject>Complex Systems</subject><subject>Curvature</subject><subject>Fluid- and Aerodynamics</subject><subject>Mathematical and Computational Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Spectrum allocation</subject><subject>Theoretical</subject><subject>Traveling waves</subject><issn>0003-9527</issn><issn>1432-0673</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp9kEFLAzEUhIMoWKt_wFPAc_QlL5tsjlKsFSoerOeQ3WTrlrpbk12L_75bV_Dm4TEMzMyDj5BrDrccQN8lAAEZA26GkwIZnpAJlygYKI2nZAIAyEwm9Dm5SGlztALVhOSL4Dx1jacrV2_p6y4En2hb0efgGjrr45fr-hjofNvu6b7u3um8jWXdrC_JWeW2KVz96pS8zR9WswVbvjw-ze6XrERuOhZyyCsIRjltPBSIRqNzTsmggjJZAZJ7idJrKfKi9FzhYE2Ry7LKdekcTsnNuLuL7WcfUmc3bR-b4aUVIjOcC63UkBJjqoxtSjFUdhfrDxe_LQd7JGRHQnYgZH8IWRxKOJbSEG7WIf5N_9M6ADk1Zos</recordid><startdate>2020</startdate><enddate>2020</enddate><creator>Gao, Hongwei</creator><creator>Kim, Inwon</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope><orcidid>https://orcid.org/0000-0003-2766-589X</orcidid></search><sort><creationdate>2020</creationdate><title>Head and Tail Speeds of Mean Curvature Flow with Forcing</title><author>Gao, Hongwei ; Kim, Inwon</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-e808f0e96a79d0b33973aaa64e6e695b041d434d7428bcd163d439b84cf87caa3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Classical Mechanics</topic><topic>Complex Systems</topic><topic>Curvature</topic><topic>Fluid- and Aerodynamics</topic><topic>Mathematical and Computational Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Spectrum allocation</topic><topic>Theoretical</topic><topic>Traveling waves</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gao, Hongwei</creatorcontrib><creatorcontrib>Kim, Inwon</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Archive for rational mechanics and analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gao, Hongwei</au><au>Kim, Inwon</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Head and Tail Speeds of Mean Curvature Flow with Forcing</atitle><jtitle>Archive for rational mechanics and analysis</jtitle><stitle>Arch Rational Mech Anal</stitle><date>2020</date><risdate>2020</risdate><volume>235</volume><issue>1</issue><spage>287</spage><epage>354</epage><pages>287-354</pages><issn>0003-9527</issn><eissn>1432-0673</eissn><abstract>In this paper, we investigate the large time behavior of interfaces moving with motion law
V
=
-
κ
+
g
(
x
)
, where
g
is positive, Lipschitz and
Z
n
-periodic. We show that the behavior of the interface can be characterized by its head and tail speeds
s
¯
and
s
̲
, which only depend on its overall direction of propagation
ν
. We discuss the large time behavior of the moving interface in terms of
s
¯
and
s
̲
, which is shown to vary continuously in
ν
. In the laminar setting we show that when
s
¯
>
s
̲
there exists an unbounded stationary solution as well as localized traveling waves with different speeds.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00205-019-01423-3</doi><tpages>68</tpages><orcidid>https://orcid.org/0000-0003-2766-589X</orcidid></addata></record> |
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| ispartof | Archive for rational mechanics and analysis, 2020, Vol.235 (1), p.287-354 |
| issn | 0003-9527 1432-0673 |
| language | eng |
| recordid | cdi_proquest_journals_2259112766 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Classical Mechanics Complex Systems Curvature Fluid- and Aerodynamics Mathematical and Computational Physics Physics Physics and Astronomy Spectrum allocation Theoretical Traveling waves |
| title | Head and Tail Speeds of Mean Curvature Flow with Forcing |
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