Lipschitz stability in the determination of the principal part of a parabolic equation
ESAIM: Control, Optimisation and Calculus of Variations, Volume 15 (2009) no. 3, pp. 525-554.

Let y(h)(t,x) be one solution to

t y(t,x)- i,j=1 n j (a ij (x) i y(t,x))=h(t,x),0<t<T,xΩ
with a non-homogeneous term h, and y| (0,T)×Ω =0, where Ω n is a bounded domain. We discuss an inverse problem of determining n(n+1)/2 unknown functions a ij by { ν y(h )| (0,T)×Γ 0 , y(h )(θ,·)} 1 0 after selecting input sources h 1 ,...,h 0 suitably, where Γ 0 is an arbitrary subboundary, ν denotes the normal derivative, 0<θ<T and 0 . In the case of 0 =(n+1) 2 n/2, we prove the Lipschitz stability in the inverse problem if we choose (h 1 ,...,h 0 ) from a set {C 0 ((0,T)×ω)} 0 with an arbitrarily fixed subdomain ωΩ. Moreover we can take 0 =(n+3)n/2 by making special choices for h , 1 0 . The proof is based on a Carleman estimate.

DOI: 10.1051/cocv:2008043
Classification: 35R30, 35K20
Keywords: inverse parabolic problem, Carleman estimate, Lipschitz stability
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     title = {Lipschitz stability in the determination of the principal part of a parabolic equation},
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     publisher = {EDP-Sciences},
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Yuan, Ganghua; Yamamoto, Masahiro. Lipschitz stability in the determination of the principal part of a parabolic equation. ESAIM: Control, Optimisation and Calculus of Variations, Volume 15 (2009) no. 3, pp. 525-554. doi : 10.1051/cocv:2008043. http://www.numdam.org/articles/10.1051/cocv:2008043/

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