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July/August 2019 Dispersive mixed-order systems in $L^p$-Sobolev spaces and application to the thermoelastic plate equation
Robert Denk, Felix Hummel
Adv. Differential Equations 24(7/8): 377-406 (July/August 2019).

Abstract

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.

Citation

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Robert Denk. Felix Hummel. "Dispersive mixed-order systems in $L^p$-Sobolev spaces and application to the thermoelastic plate equation." Adv. Differential Equations 24 (7/8) 377 - 406, July/August 2019.

Information

Published: July/August 2019
First available in Project Euclid: 2 May 2019

zbMATH: 07197891
MathSciNet: MR3945766

Subjects:
Primary: 35E15, 35M31, 35S10

Rights: Copyright © 2019 Khayyam Publishing, Inc.

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Vol.24 • No. 7/8 • July/August 2019
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