Well-posedness, smooth dependence and centre manifold reduction for a semilinear hyperbolic system from laser dynamics
We prove existence, uniqueness, regularity and smooth dependence of the weak solution on the initial data for a semilinear, first order, dissipative hyperbolic system with discontinuous coefficients. Such hyperbolic systems have successfully been used to model the dynamics of distributed feedback mu...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2007-05, Vol.30 (8), p.931-960 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Lichtner, Mark Radziunas, Mindaugas Recke, Lutz |
| description | We prove existence, uniqueness, regularity and smooth dependence of the weak solution on the initial data for a semilinear, first order, dissipative hyperbolic system with discontinuous coefficients. Such hyperbolic systems have successfully been used to model the dynamics of distributed feedback multisection semiconductor lasers. We show that in a function space of continuous functions the weak solutions generate a smooth skew product semiflow. Using slow fast structure and dissipativity we prove the existence of smooth exponentially attracting invariant centre manifolds for the non‐autonomous model. Copyright © 2006 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/mma.816 |
| format | Article |
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Such hyperbolic systems have successfully been used to model the dynamics of distributed feedback multisection semiconductor lasers. We show that in a function space of continuous functions the weak solutions generate a smooth skew product semiflow. Using slow fast structure and dissipativity we prove the existence of smooth exponentially attracting invariant centre manifolds for the non‐autonomous model. 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Meth. Appl. Sci</addtitle><description>We prove existence, uniqueness, regularity and smooth dependence of the weak solution on the initial data for a semilinear, first order, dissipative hyperbolic system with discontinuous coefficients. Such hyperbolic systems have successfully been used to model the dynamics of distributed feedback multisection semiconductor lasers. We show that in a function space of continuous functions the weak solutions generate a smooth skew product semiflow. Using slow fast structure and dissipativity we prove the existence of smooth exponentially attracting invariant centre manifolds for the non‐autonomous model. Copyright © 2006 John Wiley & Sons, Ltd.</description><subject>discontinuous coefficients</subject><subject>Exact sciences and technology</subject><subject>existence</subject><subject>existence of smooth invariant centre manifolds</subject><subject>existence, uniqueness, regularity of weak solutions</subject><subject>Global analysis, analysis on manifolds</subject><subject>laser dynamics</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>non-autonomous system</subject><subject>Partial differential equations</subject><subject>regularity of weak solutions</subject><subject>Sciences and techniques of general use</subject><subject>smooth dependence on data</subject><subject>smooth semiflow property</subject><subject>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</subject><subject>uniqueness</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNp1kM1u1TAQRiNEJS4F8QreAAua1k7i2F5WFS2I3rIBtWJj-Tpj1eCf1JMLzduTKhWsuhp90tGR5lTVG0aPGaXNSYzmWLL-WbVhVKmadaJ_Xm0oE7TuGta9qF4i_qSUSsaaTfX7GkKox4wwJEA8Ihhznm7JACOkAZIFYtJALKSpAIkmeZfDQAoMezv5nIjLhRiCEH3wCUwht_MIZZeDtwRnnCASV3IkwSAUMszJRG_xVXXgTEB4_XgPq-_nH7-dfaovv158Pju9rG3b074WVHXKKm65gA7sTnatdDvecccVE9JwIziVkjm5jJ2DoQer5MOijNOmbQ-rd6t3LPluDzjp6NEuL5sEeY-6UapXUjQL-H4FbcmIBZwei4-mzJpR_dBVL1310nUh3z4qDVoTXDHJevyPy14xybuF-7Byf3yA-Smd3m5PV2u90n5Jdv-PNuWX7kUruL6-utA351_49qb5oWX7FztRlo4</recordid><startdate>20070525</startdate><enddate>20070525</enddate><creator>Lichtner, Mark</creator><creator>Radziunas, Mindaugas</creator><creator>Recke, Lutz</creator><general>John Wiley & Sons, Ltd</general><general>Wiley</general><general>Teubner</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope></search><sort><creationdate>20070525</creationdate><title>Well-posedness, smooth dependence and centre manifold reduction for a semilinear hyperbolic system from laser dynamics</title><author>Lichtner, Mark ; Radziunas, Mindaugas ; Recke, Lutz</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3606-70949c95c57e4ecb8438fb545f59178a5a750881f878abfed6ec98f8780150233</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>discontinuous coefficients</topic><topic>Exact sciences and technology</topic><topic>existence</topic><topic>existence of smooth invariant centre manifolds</topic><topic>existence, uniqueness, regularity of weak solutions</topic><topic>Global analysis, analysis on manifolds</topic><topic>laser dynamics</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>non-autonomous system</topic><topic>Partial differential equations</topic><topic>regularity of weak solutions</topic><topic>Sciences and techniques of general use</topic><topic>smooth dependence on data</topic><topic>smooth semiflow property</topic><topic>Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds</topic><topic>uniqueness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lichtner, Mark</creatorcontrib><creatorcontrib>Radziunas, Mindaugas</creatorcontrib><creatorcontrib>Recke, Lutz</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lichtner, Mark</au><au>Radziunas, Mindaugas</au><au>Recke, Lutz</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Well-posedness, smooth dependence and centre manifold reduction for a semilinear hyperbolic system from laser dynamics</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><addtitle>Math. Meth. Appl. Sci</addtitle><date>2007-05-25</date><risdate>2007</risdate><volume>30</volume><issue>8</issue><spage>931</spage><epage>960</epage><pages>931-960</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><coden>MMSCDB</coden><abstract>We prove existence, uniqueness, regularity and smooth dependence of the weak solution on the initial data for a semilinear, first order, dissipative hyperbolic system with discontinuous coefficients. Such hyperbolic systems have successfully been used to model the dynamics of distributed feedback multisection semiconductor lasers. We show that in a function space of continuous functions the weak solutions generate a smooth skew product semiflow. Using slow fast structure and dissipativity we prove the existence of smooth exponentially attracting invariant centre manifolds for the non‐autonomous model. Copyright © 2006 John Wiley & Sons, Ltd.</abstract><cop>Chichester, UK</cop><pub>John Wiley & Sons, Ltd</pub><doi>10.1002/mma.816</doi><tpages>30</tpages></addata></record> |
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| subjects | discontinuous coefficients Exact sciences and technology existence existence of smooth invariant centre manifolds existence, uniqueness, regularity of weak solutions Global analysis, analysis on manifolds laser dynamics Mathematical analysis Mathematics non-autonomous system Partial differential equations regularity of weak solutions Sciences and techniques of general use smooth dependence on data smooth semiflow property Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds uniqueness |
| title | Well-posedness, smooth dependence and centre manifold reduction for a semilinear hyperbolic system from laser dynamics |
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