Abstract
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.
| 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
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Lp theory for the linear thermoelastic plate equations in bounded and exterior domains. / Denk, Robert; Racke, Reinhard; Shibata, Yoshihiro.
In: Advances in Differential Equations, Vol. 14, No. 7-8, 2009, p. 685-715.Research output: Contribution to journal › Article
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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 -