$L^p$-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 |
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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 |
| Summary: | 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. |
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| ISSN: | 1072-6691 |