Advances in Differential Equations

Dispersive mixed-order systems in $L^p$-Sobolev spaces and application to the thermoelastic plate equation

Robert Denk and Felix Hummel

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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.

Article information

Source
Adv. Differential Equations, Volume 24, Number 7/8 (2019), 377-406.

Dates
First available in Project Euclid: 2 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.ade/1556762453

Mathematical Reviews number (MathSciNet)
MR3945766

Subjects
Primary: 35M31: Initial value problems for systems of mixed type 35S10: Initial value problems for pseudodifferential operators 35E15: Initial value problems

Citation

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


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