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Dispersive mixed-order systems in L<sup>p</sup>-Sobolev spaces and application to the thermoelastic plate equation

Dispersive mixed-order systems in Lp-Sobolev spaces and application to the thermoelastic plate equation

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DENK, Robert, Felix HUMMEL, 2019. Dispersive mixed-order systems in Lp-Sobolev spaces and application to the thermoelastic plate equation. In: Advances in Differential Equations. 24(7/8), pp. 377-406. ISSN 1079-9389

@article{Denk2019Dispe-35824.2, title={Dispersive mixed-order systems in Lp-Sobolev spaces and application to the thermoelastic plate equation}, url={https://projecteuclid.org/euclid.ade/1556762453}, year={2019}, number={7/8}, volume={24}, issn={1079-9389}, journal={Advances in Differential Equations}, pages={377--406}, author={Denk, Robert and Hummel, Felix} }

We study dispersive mixed-order systems of pseudodifferential operators in the setting of L<sup>p</sup>-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<sup>p</sup>-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. Hummel, Felix Hummel, Felix Denk, Robert Dispersive mixed-order systems in L<sup>p</sup>-Sobolev spaces and application to the thermoelastic plate equation eng 2019-07-17T13:00:40Z Denk, Robert 2019-07-17T13:00:40Z 2019 terms-of-use

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