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

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  • 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.

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


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