### Abstract

The paper is concerned with linear thermoelastic plate equations in the half-space R_{+}^{n} = {x = (x_{1},..., x_{n}) | x_{n} > 0}: u_{tt} + Δ^{2}u + Δθ = 0 and θ_{t} - Δθ - Δθu_{t} = 0 in R_{+}^{n} × (0, ∞), subject to the boundary condition: u|_{xn}=0 = D_{n} u|_{x} _{n}=0 = θ|_{xn}=0 = 0 and initial condition: (u,D_{t}u,θ)|_{t=0} = (u_{0},v_{0}, θ_{0}) ∈ H_{p} = W_{p,D}^{2} × L_{P} × L_{P}, where W_{p,D}^{2} = {u ∈ W_{p}^{2} | u|_{Xn}=0 = D _{n}u|_{xn}=0 = 0}. We show that for any p ∈ (1, infin;), the associated semigroup {T(t)}_{t≥0} is analytic in the underlying space H_{p}. Moreover, a solution (u, θ) satisfies the estimates: ||∇^{j}(∇^{2}u(·, t), u _{t}(·, t), θ(·, t))||_{L} _{q}(R_{+}^{n}) ≤ c_{p,q}t-1\2-n\2(1\p-1\q) ||(∇^{2}u_{0},V_{0}, θ_{0})|| _{Lq}(R_{+}^{n}) (t > 0) for j = 0, 1, 2 provided that 1 < p ≤ q ≤ ∞ when j = 0, 1 and that 1 < p ≤ q < ∞ when j = 2, where ∇^{j} stands for space gradient of order j.

Original language | English |
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Pages (from-to) | 971-1011 |

Number of pages | 41 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 61 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 Oct 1 |

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### Keywords

- Half space
- L analytic semigroup
- L-l decay estimate
- Resolvent estimate
- Thermoelastic plate equations
- Whole space

### ASJC Scopus subject areas

- Mathematics(all)