On the Lp analytic semigroup associated with the linear thermoelastic plate equations in the half-space

Yuka Naito, Yoshihiro Shibata

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The paper is concerned with linear thermoelastic plate equations in the half-space R+n = {x = (x1,..., xn) | xn > 0}: utt + Δ2u + Δθ = 0 and θt - Δθ - Δθut = 0 in R+n × (0, ∞), subject to the boundary condition: u|xn=0 = Dn u|x n=0 = θ|xn=0 = 0 and initial condition: (u,Dtu,θ)|t=0 = (u0,v0, θ0) ∈ Hp = Wp,D2 × LP × LP, where Wp,D2 = {u ∈ Wp2 | u|Xn=0 = D nu|xn=0 = 0}. We show that for any p ∈ (1, infin;), the associated semigroup {T(t)}t≥0 is analytic in the underlying space Hp. Moreover, a solution (u, θ) satisfies the estimates: ||∇j(∇2u(·, t), u t(·, t), θ(·, t))||L q(R+n) ≤ cp,qt-1\2-n\2(1\p-1\q) ||(∇2u0,V0, θ0)|| 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 languageEnglish
Pages (from-to)971-1011
Number of pages41
JournalJournal of the Mathematical Society of Japan
Volume61
Issue number4
DOIs
Publication statusPublished - 2009 Oct 1

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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