$L^p$-resolvent estimates and time decay for generalized thermoelastic plate equations
We consider the Cauchy problem for a coupled system generalizing the thermoelastic plate equations. First we prove resolvent estimates for the stationary operator and conclude the analyticity of the associated semigroup in $L^p$-spaces, $1<p<infty$, for certain values of the parameters of...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2006-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2006/48/abstr.html |
| _version_ | 1828163013456166912 |
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| author | Robert Denk Reinhard Racke |
| author_facet | Robert Denk Reinhard Racke |
| author_sort | Robert Denk |
| collection | DOAJ |
| description | We consider the Cauchy problem for a coupled system generalizing the thermoelastic plate equations. First we prove resolvent estimates for the stationary operator and conclude the analyticity of the associated semigroup in $L^p$-spaces, $1<p<infty$, for certain values of the parameters of the system; here the Newton polygon method is used. Then we prove decay rates of the $L^q(mathbb{R}^n)$-norms of solutions, $2leq qleqinfty$, as time tends to infinity. |
| first_indexed | 2024-04-12T01:03:50Z |
| format | Article |
| id | doaj.art-c3b5f5ec1ac447f18a701d2f52f43b6f |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T01:03:50Z |
| publishDate | 2006-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-c3b5f5ec1ac447f18a701d2f52f43b6f2022-12-22T03:54:22ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912006-04-01200648116$L^p$-resolvent estimates and time decay for generalized thermoelastic plate equationsRobert DenkReinhard RackeWe consider the Cauchy problem for a coupled system generalizing the thermoelastic plate equations. First we prove resolvent estimates for the stationary operator and conclude the analyticity of the associated semigroup in $L^p$-spaces, $1<p<infty$, for certain values of the parameters of the system; here the Newton polygon method is used. Then we prove decay rates of the $L^q(mathbb{R}^n)$-norms of solutions, $2leq qleqinfty$, as time tends to infinity.http://ejde.math.txstate.edu/Volumes/2006/48/abstr.htmlAnalytic semigroup in $L^p$polynomial decay ratesCauchy problem. |
| spellingShingle | Robert Denk Reinhard Racke $L^p$-resolvent estimates and time decay for generalized thermoelastic plate equations Electronic Journal of Differential Equations Analytic semigroup in $L^p$ polynomial decay rates Cauchy problem. |
| title | $L^p$-resolvent estimates and time decay for generalized thermoelastic plate equations |
| title_full | $L^p$-resolvent estimates and time decay for generalized thermoelastic plate equations |
| title_fullStr | $L^p$-resolvent estimates and time decay for generalized thermoelastic plate equations |
| title_full_unstemmed | $L^p$-resolvent estimates and time decay for generalized thermoelastic plate equations |
| title_short | $L^p$-resolvent estimates and time decay for generalized thermoelastic plate equations |
| title_sort | l p resolvent estimates and time decay for generalized thermoelastic plate equations |
| topic | Analytic semigroup in $L^p$ polynomial decay rates Cauchy problem. |
| url | http://ejde.math.txstate.edu/Volumes/2006/48/abstr.html |
| work_keys_str_mv | AT robertdenk lpresolventestimatesandtimedecayforgeneralizedthermoelasticplateequations AT reinhardracke lpresolventestimatesandtimedecayforgeneralizedthermoelasticplateequations |