Issue |
ESAIM: COCV
Volume 15, Number 3, July-September 2009
|
|
---|---|---|
Page(s) | 525 - 554 | |
DOI | https://doi.org/10.1051/cocv:2008043 | |
Published online | 19 July 2008 |
Lipschitz stability in the determination of the principal part of a parabolic equation
1
Department of Mathematical Sciences, The University of Tokyo,
Komaba Meguro, Tokyo, 153-8914, Japan. g_h_yuan@hotmail.com; myama@ms.u-tokyo.ac.jp
2
School of Mathematics & Statistics, Northeast Normal University,
Changchun, Jilin, 130024, P. R. China.
Received:
7
March
2007
Revised:
31
December
2007
Let y(h)(t,x) be one solution to
with a non-homogeneous term h, and
,
where
is a bounded domain. We discuss an inverse problem
of determining n(n+1)/2 unknown functions aij by
,
after selecting input sources
suitably, where
is an arbitrary subboundary,
denotes the normal derivative,
and
. In the case of
, we prove
the Lipschitz stability in the inverse problem if we choose
from a set
with an arbitrarily fixed subdomain
. Moreover we can take
by making special choices for
,
. The proof is based on a Carleman
estimate.
Mathematics Subject Classification: 35R30 / 35K20
Key words: Inverse parabolic problem / Carleman estimate / Lipschitz stability
© EDP Sciences, SMAI, 2008
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