Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data
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June 2019, 8(2): 301-313. doi: 10.3934/eect.2019016
Generation of semigroups for the thermoelastic plate equation with free boundary conditions
Robert Denk 1, and Yoshihiro Shibata 2,
University of Konstanz, Department of Mathematics and Statistics, 78457 Konstanz, Germany
Department of Mathematical Sciences, School of Science and Engineering, Waseda University, Ohkobu 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan
Received June 2018 Revised October 2018 Published June 2019 Early access March 2019
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.
Keywords: Thermoelastic plate equations, operator-valued Fourier multipliers, generation of analytic semigroups.
Mathematics Subject Classification: Primary: 35K35, 35J40; Secondary: 42B15.
Citation: Robert Denk, Yoshihiro Shibata. Generation of semigroups for the thermoelastic plate equation with free boundary conditions. Evolution Equations & Control Theory, 2019, 8 (2) : 301-313. doi: 10.3934/eect.2019016
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Robert Denk Yoshihiro Shibata