### 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 |
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Pages (from-to) | 685-715 |

Number of pages | 31 |

Journal | Advances in Differential Equations |

Volume | 14 |

Issue number | 7-8 |

Publication status | Published - 2009 Dec 1 |

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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.