Lubrication Approximation for Thin Viscous Films: Asymptotic Behavior of Nonnegative Solutions
We use standard regularized equations and adapted entropy functionals to prove exponential asymptotic decay in the H 1 norm for nonnegative weak solutions of fourth-order nonlinear degenerate parabolic equations of lubrication approximation for thin viscous film type. The weak solutions considered a...
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| Veröffentlicht in: | Communications in partial differential equations 2007-08, Vol.32 (7), p.1147-1172 |
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| container_title | Communications in partial differential equations |
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| creator | Tudorascu, Adrian |
| description | We use standard regularized equations and adapted entropy functionals to prove exponential asymptotic decay in the H
1
norm for nonnegative weak solutions of fourth-order nonlinear degenerate parabolic equations of lubrication approximation for thin viscous film type. The weak solutions considered arise as limits of solutions for the regularized problems. Relaxed problems, with second-order nonlinear terms of porous media type are also successfully treated by the same means. The problems investigated here are one-dimensional in space, with power-law nonlinearities. Our approach is direct and natural, as it is adapted to deal with the more complex nonlinear terms occurring in the regularized, approximating problems. |
| doi_str_mv | 10.1080/03605300600987272 |
| format | Article |
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1
norm for nonnegative weak solutions of fourth-order nonlinear degenerate parabolic equations of lubrication approximation for thin viscous film type. The weak solutions considered arise as limits of solutions for the regularized problems. Relaxed problems, with second-order nonlinear terms of porous media type are also successfully treated by the same means. The problems investigated here are one-dimensional in space, with power-law nonlinearities. Our approach is direct and natural, as it is adapted to deal with the more complex nonlinear terms occurring in the regularized, approximating problems.</description><identifier>ISSN: 0360-5302</identifier><identifier>EISSN: 1532-4133</identifier><identifier>DOI: 10.1080/03605300600987272</identifier><language>eng</language><publisher>Taylor & Francis Group</publisher><subject>Asymptotic decay ; Entropy dissipation ; Exponential decay ; Fourth-order nonlinear parabolic equation</subject><ispartof>Communications in partial differential equations, 2007-08, Vol.32 (7), p.1147-1172</ispartof><rights>Copyright Taylor & Francis Group, LLC 2007</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c346t-4ade87099aadd2cc02e254108ca251671087f653618f67be5fb307e2a73c1f2c3</citedby><cites>FETCH-LOGICAL-c346t-4ade87099aadd2cc02e254108ca251671087f653618f67be5fb307e2a73c1f2c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.tandfonline.com/doi/pdf/10.1080/03605300600987272$$EPDF$$P50$$Ginformaworld$$H</linktopdf><linktohtml>$$Uhttps://www.tandfonline.com/doi/full/10.1080/03605300600987272$$EHTML$$P50$$Ginformaworld$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,59645,60434</link.rule.ids></links><search><creatorcontrib>Tudorascu, Adrian</creatorcontrib><title>Lubrication Approximation for Thin Viscous Films: Asymptotic Behavior of Nonnegative Solutions</title><title>Communications in partial differential equations</title><description>We use standard regularized equations and adapted entropy functionals to prove exponential asymptotic decay in the H
1
norm for nonnegative weak solutions of fourth-order nonlinear degenerate parabolic equations of lubrication approximation for thin viscous film type. The weak solutions considered arise as limits of solutions for the regularized problems. Relaxed problems, with second-order nonlinear terms of porous media type are also successfully treated by the same means. The problems investigated here are one-dimensional in space, with power-law nonlinearities. Our approach is direct and natural, as it is adapted to deal with the more complex nonlinear terms occurring in the regularized, approximating problems.</description><subject>Asymptotic decay</subject><subject>Entropy dissipation</subject><subject>Exponential decay</subject><subject>Fourth-order nonlinear parabolic equation</subject><issn>0360-5302</issn><issn>1532-4133</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNqFkEFOwzAQRS0EEqVwAHa-QGBsJ3GC2JSKAlIFCwpLItexqVESR7Zb2tvjKuwqxGpmNP_90R-ELglcESjgGlgOGQPIAcqCU06P0IhkjCYpYewYjfb7JAroKTrz_guAFLRMR-hjvl46I0UwtsOTvnd2a9ph0tbhxcp0-N14adcez0zT-hs88bu2DzYYie_USmxM1FmNn23Xqc-IbhR-tc167-HP0YkWjVcXv3WM3mb3i-ljMn95eJpO5olkaR6SVNSq4FCWQtQ1lRKoolkag0lBM5Lz2HGdZywnhc75UmV6yYArKjiTRFPJxogMvtJZ753SVe9iDrerCFT7B1UHD4oMHxjTxait-Lauqasgdo112olOGn9IVWEbInn7L8n-PvwDw5V-4Q</recordid><startdate>20070809</startdate><enddate>20070809</enddate><creator>Tudorascu, Adrian</creator><general>Taylor & Francis Group</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20070809</creationdate><title>Lubrication Approximation for Thin Viscous Films: Asymptotic Behavior of Nonnegative Solutions</title><author>Tudorascu, Adrian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c346t-4ade87099aadd2cc02e254108ca251671087f653618f67be5fb307e2a73c1f2c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Asymptotic decay</topic><topic>Entropy dissipation</topic><topic>Exponential decay</topic><topic>Fourth-order nonlinear parabolic equation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tudorascu, Adrian</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tudorascu, Adrian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Lubrication Approximation for Thin Viscous Films: Asymptotic Behavior of Nonnegative Solutions</atitle><jtitle>Communications in partial differential equations</jtitle><date>2007-08-09</date><risdate>2007</risdate><volume>32</volume><issue>7</issue><spage>1147</spage><epage>1172</epage><pages>1147-1172</pages><issn>0360-5302</issn><eissn>1532-4133</eissn><abstract>We use standard regularized equations and adapted entropy functionals to prove exponential asymptotic decay in the H
1
norm for nonnegative weak solutions of fourth-order nonlinear degenerate parabolic equations of lubrication approximation for thin viscous film type. The weak solutions considered arise as limits of solutions for the regularized problems. Relaxed problems, with second-order nonlinear terms of porous media type are also successfully treated by the same means. The problems investigated here are one-dimensional in space, with power-law nonlinearities. Our approach is direct and natural, as it is adapted to deal with the more complex nonlinear terms occurring in the regularized, approximating problems.</abstract><pub>Taylor & Francis Group</pub><doi>10.1080/03605300600987272</doi><tpages>26</tpages></addata></record> |
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| ispartof | Communications in partial differential equations, 2007-08, Vol.32 (7), p.1147-1172 |
| issn | 0360-5302 1532-4133 |
| language | eng |
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| source | Taylor & Francis Journals Complete |
| subjects | Asymptotic decay Entropy dissipation Exponential decay Fourth-order nonlinear parabolic equation |
| title | Lubrication Approximation for Thin Viscous Films: Asymptotic Behavior of Nonnegative Solutions |
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