Advances in Differential Equations
- Adv. Differential Equations
- Volume 24, Number 7/8 (2019), 377-406.
Dispersive mixed-order systems in $L^p$-Sobolev spaces and application to the thermoelastic plate equation
We study dispersive mixed-order systems of pseudodifferential operators in the setting of $L^p$-Sobolev spaces. Under the weak condition of quasi-hyperbolicity, these operators generate a semigroup in the space of tempered distributions. However, if the basic space is a tuple of $L^p$-Sobolev spaces, a strongly continuous semigroup is in many cases only generated if $p=2$ or $n=1$. The results are applied to the linear thermoelastic plate equation with and without inertial term and with Fourier's or Maxwell-Cattaneo's law of heat conduction.
Adv. Differential Equations, Volume 24, Number 7/8 (2019), 377-406.
First available in Project Euclid: 2 May 2019
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Mathematical Reviews number (MathSciNet)
Denk, Robert; Hummel, Felix. Dispersive mixed-order systems in $L^p$-Sobolev spaces and application to the thermoelastic plate equation. Adv. Differential Equations 24 (2019), no. 7/8, 377--406. https://projecteuclid.org/euclid.ade/1556762453