Lipschitz stability in the lateral Cauchy problem for elasticity system
Cheng, Jin Isakov, Victor Yamamoto, Masahiro Zhou, Qi
Cheng, Jin
Isakov, Victor
Yamamoto, Masahiro
Zhou, Qi
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2003-08-01
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Cheng, Jin; Isakov, Victor; Yamamoto, Masahiro; Zhou, Qi. 2003. Lipschitz stability in the lateral Cauchy problem for elasticity system. J. Math. Kyoto Univ. Volume 43, Number 3 (2003), 475-501.
Abstract
We consider the isotropic elasticity system:
ρ∂2
t u − μ(Δu + ∇(∇Tu))−∇(λ∇Tu)
−
3
X
j=1
∇μ · (∇uj + ∂ju)ej = 0 in Ω× (0, T)
for the displacement vector u = (u1, u2, u3) depending on x ∈ Ω and
t ∈ (0, T) where Ω is a bounded domain in R3 with the C2-boundary,
and we assume the density ρ ∈ C2(Ω× [0, T]) and the Lam´e parameters
μ, λ ∈ C3(Ω × [0, T]). We will give Lipschitz stability estimates for
solutions u to the above elasticity system with the lateral boundary
data
u = g on ∂Ω × (0, T), ∂νu = h on Γ × (0, T)
where Γ is some part of ∂Ω. Our proof is based on (1) a Carleman
estimate with boundary data, (2) cut-off technique, and (3) principal
diagonalization of the Lam´e system.
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Open Access. Click on the link to access the article at the publisher's website.
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Kyoto University
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Kyoto Journal of Mathematics;v.43 no.3
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0023-608X