### Abstract

The paper is concerned with linear thermoelastic plate equations in a domain Ω: utt + Δ^{2}u + ΔΘ = 0 and Θ_{t} - ΔΘ - Δu_{t} =0 in Ω × (0, ∞), subject to the Dirichlet boundary condition u|r = Dvu|γ = Θ|γ = 0 and initial condition (u,u_{t},Θ)|_{t=0} = (u_{0},v_{0},Θ_{0}) ∈ W^{2}
_{p},D(Ω) × L_{p} × L_{p}. Here, ω is a bounded or exterior domain in ℝ^{n} (n > 2). We assume that the boundary Γ of Ω is a C^{4} hypersurface and we define W^{2}
_{P},D by the formula W^{2}
_{P},D = {u ∈ W^{2}
_{p}: u|γ = D_{v}u|γ = 0}. We show that, for any p ∈ (l,∞), the associated semigroup {T(t)}t>o is analytic. Moreover, if fi is bounded, then {T(t)}_{t≥o} is exponentially stable.

Original language | English |
---|---|

Pages (from-to) | 685-715 |

Number of pages | 31 |

Journal | Advances in Differential Equations |

Volume | 14 |

Issue number | 7-8 |

Publication status | Published - 2009 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

_{p}theory for the linear thermoelastic plate equations in bounded and exterior domains.

*Advances in Differential Equations*,

*14*(7-8), 685-715.

**L _{p} theory for the linear thermoelastic plate equations in bounded and exterior domains.** / Denk, Robert; Racke, Reinhard; Shibata, Yoshihiro.

Research output: Contribution to journal › Article

_{p}theory for the linear thermoelastic plate equations in bounded and exterior domains',

*Advances in Differential Equations*, vol. 14, no. 7-8, pp. 685-715.

_{p}theory for the linear thermoelastic plate equations in bounded and exterior domains. Advances in Differential Equations. 2009;14(7-8):685-715.

}

TY - JOUR

T1 - Lp theory for the linear thermoelastic plate equations in bounded and exterior domains

AU - Denk, Robert

AU - Racke, Reinhard

AU - Shibata, Yoshihiro

PY - 2009

Y1 - 2009

N2 - The paper is concerned with linear thermoelastic plate equations in a domain Ω: utt + Δ2u + ΔΘ = 0 and Θt - ΔΘ - Δut =0 in Ω × (0, ∞), subject to the Dirichlet boundary condition u|r = Dvu|γ = Θ|γ = 0 and initial condition (u,ut,Θ)|t=0 = (u0,v0,Θ0) ∈ W2 p,D(Ω) × Lp × Lp. Here, ω is a bounded or exterior domain in ℝn (n > 2). We assume that the boundary Γ of Ω is a C4 hypersurface and we define W2 P,D by the formula W2 P,D = {u ∈ W2 p: u|γ = Dvu|γ = 0}. We show that, for any p ∈ (l,∞), the associated semigroup {T(t)}t>o is analytic. Moreover, if fi is bounded, then {T(t)}t≥o is exponentially stable.

AB - The paper is concerned with linear thermoelastic plate equations in a domain Ω: utt + Δ2u + ΔΘ = 0 and Θt - ΔΘ - Δut =0 in Ω × (0, ∞), subject to the Dirichlet boundary condition u|r = Dvu|γ = Θ|γ = 0 and initial condition (u,ut,Θ)|t=0 = (u0,v0,Θ0) ∈ W2 p,D(Ω) × Lp × Lp. Here, ω is a bounded or exterior domain in ℝn (n > 2). We assume that the boundary Γ of Ω is a C4 hypersurface and we define W2 P,D by the formula W2 P,D = {u ∈ W2 p: u|γ = Dvu|γ = 0}. We show that, for any p ∈ (l,∞), the associated semigroup {T(t)}t>o is analytic. Moreover, if fi is bounded, then {T(t)}t≥o is exponentially stable.

UR - http://www.scopus.com/inward/record.url?scp=74849091828&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74849091828&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:74849091828

VL - 14

SP - 685

EP - 715

JO - Advances in Differential Equations

JF - Advances in Differential Equations

SN - 1079-9389

IS - 7-8

ER -