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

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

ty(t,x)-i,j=1nj(aij(x)iy(t,x))=h(t,x),0<t<T,xΩ
with a non-homogeneous term h, and y|(0,T)×Ω=0, where Ωn is a bounded domain. We discuss an inverse problem of determining n(n+1)/2 unknown functions aij by {νy(h)|(0,T)×Γ0, y(h)(θ,·)}10 after selecting input sources h1,...,h0 suitably, where Γ0 is an arbitrary subboundary, ν denotes the normal derivative, 0<θ<T and 0. In the case of 0=(n+1)2n/2, we prove the Lipschitz stability in the inverse problem if we choose (h1,...,h0) from a set {C0((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, 10. The proof is based on a Carleman estimate.

DOI : 10.1051/cocv:2008043
Classification : 35R30, 35K20
Mots-clés : inverse parabolic problem, Carleman estimate, Lipschitz stability
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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, Tome 15 (2009) no. 3, pp. 525-554. doi : 10.1051/cocv:2008043. https://www.numdam.org/articles/10.1051/cocv:2008043/

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