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

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Advances in Differential Equations. 2019, 24(7/8), pp. 377-406. ISSN 1079-9389
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We study dispersive mixed-order systems of pseudodifferential operators in the setting of Lp-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 Lp-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.

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ISO 690DENK, Robert, Felix Benjamin HUMMEL, 2019. Dispersive mixed-order systems in Lp-Sobolev spaces and application to the thermoelastic plate equation. In: Advances in Differential Equations. 2019, 24(7/8), pp. 377-406. ISSN 1079-9389
BibTex
@article{Denk2019Dispe-35824.2,
  year={2019},
  title={Dispersive mixed-order systems in L<sup>p</sup>-Sobolev spaces and application to the thermoelastic plate equation},
  url={https://projecteuclid.org/euclid.ade/1556762453},
  number={7/8},
  volume={24},
  issn={1079-9389},
  journal={Advances in Differential Equations},
  pages={377--406},
  author={Denk, Robert and Hummel, Felix Benjamin}
}
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