Generation of semigroups for the thermoelastic plate equation with free boundary conditions

Robert Denk; Yoshihiro Shibata

doi:10.3934/eect.2019016

Generation of semigroups for the thermoelastic plate equation with free boundary conditions

Robert Denk, Yoshihiro Shibata

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We consider the linear thermoelastic plate equations with free boundary conditions in uniform C4-domains, which includes the half-space, bounded and exterior domains. We show that the corresponding operator generates an analytic semigroup in Lp-spaces for all p∈(1,∞) and has maximal Lq-Lp-regularity on finite time intervals. On bounded C4 -domains, we obtain exponential stability.

Original language	English
Pages (from-to)	301-313
Number of pages	13
Journal	Evolution Equations and Control Theory
Volume	8
Issue number	2
DOIs	https://doi.org/10.3934/eect.2019016
Publication status	Published - 2019 Jun
Externally published	Yes

Keywords

Generation of analytic semigroups
Operator-valued fourier multipliers
Thermoelastic plate equations

ASJC Scopus subject areas

Modelling and Simulation
Control and Optimization
Applied Mathematics

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10.3934/eect.2019016

Cite this

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abstract = "We consider the linear thermoelastic plate equations with free boundary conditions in uniform C4-domains, which includes the half-space, bounded and exterior domains. We show that the corresponding operator generates an analytic semigroup in Lp-spaces for all p∈(1,∞) and has maximal Lq-Lp-regularity on finite time intervals. On bounded C4 -domains, we obtain exponential stability.",

keywords = "Generation of analytic semigroups, Operator-valued fourier multipliers, Thermoelastic plate equations",

author = "Robert Denk and Yoshihiro Shibata",

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AU - Shibata, Yoshihiro

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AB - We consider the linear thermoelastic plate equations with free boundary conditions in uniform C4-domains, which includes the half-space, bounded and exterior domains. We show that the corresponding operator generates an analytic semigroup in Lp-spaces for all p∈(1,∞) and has maximal Lq-Lp-regularity on finite time intervals. On bounded C4 -domains, we obtain exponential stability.

KW - Generation of analytic semigroups

KW - Operator-valued fourier multipliers

KW - Thermoelastic plate equations

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JO - Evolution Equations and Control Theory

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ER -

Generation of semigroups for the thermoelastic plate equation with free boundary conditions

Abstract

Keywords

ASJC Scopus subject areas

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