Generation of semigroups for the thermoelastic plate equation with free boundary conditions

Robert Denk; Yoshihiro Shibata

doi:10.3934/eect.2019016

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2019, Volume 8, Issue 2: 301-313. Doi: 10.3934/eect.2019016

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Generation of semigroups for the thermoelastic plate equation with free boundary conditions

Robert Denk^1, and
Yoshihiro Shibata^2,

1.
University of Konstanz, Department of Mathematics and Statistics, 78457 Konstanz, Germany
2.
Department of Mathematical Sciences, School of Science and Engineering, Waseda University, Ohkobu 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan

Received: May 31, 2018

Revised: September 30, 2018

Early access: March 2019

Published: May 2019

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Abstract

We consider the linear thermoelastic plate equations with free boundary conditions in uniform $ C^4 $-domains, which includes the half-space, bounded and exterior domains. We show that the corresponding operator generates an analytic semigroup in $ L^p $-spaces for all $ p\in(1, \infty) $ and has maximal $ L^q $-$ L^p $-regularity on finite time intervals. On bounded $ C^4 $-domains, we obtain exponential stability.

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Mathematics Subject Classification: Primary: 35K35, 35J40; Secondary: 42B15.

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