CORE
🇺🇦Â
 make metadata, not war
Services
Services overview
Explore all CORE services
Access to raw data
API
Dataset
FastSync
Content discovery
Recommender
Discovery
OAI identifiers
OAI Resolver
Managing content
Dashboard
Bespoke contracts
Consultancy services
Support us
Support us
Membership
Sponsorship
Community governance
Advisory Board
Board of supporters
Research network
About
About us
Our mission
Team
Blog
FAQs
Contact us
research
Lipschitz stability in an inverse problem for the wave equation
Authors
Lucie Baudouin
Publication date
1 June 2010
Publisher
View
on
arXiv
Abstract
We are interested in the inverse problem of the determination of the potential
p
(
x
)
,
x
∈
Ω
⊂
R
n
p(x), x\in\Omega\subset\mathbb{R}^n
p
(
x
)
,
x
∈
Ω
⊂
R
n
from the measurement of the normal derivative
∂
ν
u
\partial_\nu u
∂
ν
​
u
on a suitable part
Γ
0
\Gamma_0
Γ
0
​
of the boundary of
Ω
\Omega
Ω
, where
u
u
u
is the solution of the wave equation
∂
t
t
u
(
x
,
t
)
−
Δ
u
(
x
,
t
)
+
p
(
x
)
u
(
x
,
t
)
=
0
\partial_{tt}u(x,t)-\Delta u(x,t)+p(x)u(x,t)=0
∂
tt
​
u
(
x
,
t
)
−
Δ
u
(
x
,
t
)
+
p
(
x
)
u
(
x
,
t
)
=
0
set in
Ω
×
(
0
,
T
)
\Omega\times(0,T)
Ω
×
(
0
,
T
)
and given Dirichlet boundary data. More precisely, we will prove local uniqueness and stability for this inverse problem and the main tool will be a global Carleman estimate, result also interesting by itself
Similar works
Full text
Available Versions
HAL-INSA Toulouse
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:HAL:hal-00598876v1
Last time updated on 07/05/2019
Scientific Publications of the University of Toulouse II Le Mirail
See this paper in CORE
Go to the repository landing page
Download from data provider
oai:HAL:hal-00598876v1
Last time updated on 06/12/2019